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Compressive Sensing (CS) has well boosted massive random access protocols over the last decade. Usually, on physical layer, the protocols employ some fat matrix with the property that sparse vectors in the much larger column space domain can still be recovered. This, in turn, greatly reduces the chances of collisions between access devices. This basic scheme has meanwhile been enhanced in various directions but the system cannot operate in overload regime, i.e. sustain significantly more users than the row dimension of the fat matrix dictates. In this paper, we take a different route and apply an orthogonal DFT basis as it is used in OFDM, but subdivide its image into so-called sub-channels and let each sub-channel take only a fraction of the load. In a random fashion the subdivision is consecutively applied over a suitable number of time-slots. Within the time-slots the users will not change their sub-channel assignment and send in parallel the data. Activity detection is carried out jointly across time-slots in each of the sub-channels. For such system design we derive three rather fundamental results: i) First, we prove that the subdivision can be driven to the extent that the activity in each sub-channel is sparse by design. An effect that we call sparsity capture effect . ii) Second, we prove that effectively the system can sustain any overload situation relative to the DFT dimension, i.e. detection failure of active and non-active users can be kept below any desired threshold regardless of the number of users. The only price to pay is delay, i.e. the number of time-slots over which cross-detection is performed. We achieve this by jointly exploring the effect of measure concentration in time and frequency and careful system parameter scaling. iii) Third, we prove that parallel to activity detection active users can carry one symbol per pilot and time-slot so it supports so-called one-shot messaging . The key to proving these results are new concentration result

This paper presents novel cascaded channel estimation techniques for an intelligent reflecting surface-aided multiple-input multiple-output system. Motivated by the channel angular sparsity at higher frequency bands, the channel estimation problem is formulated as a sparse vector recovery problem with an inherent Kronecker structure. We solve the problem using the sparse Bayesian learning framework which leads to a non-convex optimization problem. We offer two solution techniques to the problem based on alternating minimization and singular value decomposition. Our simulation results illustrate the superior performance of our methods in terms of accuracy and run time compared with the existing works., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Signal Processing Systems

The fast and reliable processing of medical images is of paramount importance to adequately generate data to feed machine learning algorithms that can prevent and diagnose health issues. Here, different compressed sensing techniques applied to magnetic resonance imaging are benchmarked as a means to reduce the acquisition time spent in the collection of data and signals that form the image. It is shown that by using these techniques, it is possible to reduce the number of signals needed and, therefore, substantially decrease the time to acquire the measurements. To this end, different algorithms are considered and compared: the iterative re-weighted least squares, the iterative soft thresholding algorithm, the iterative hard thresholding algorithm, the primal dual algorithm and the log barrier algorithm. Such algorithms have been implemented in different analysis programs that have been used to perform the reconstruction of the images, and it was found that the iterative soft thresholding algorithm gives the optimal results. It is found that the images obtained with this algorithm have lower quality than the original ones, but in any case, the quality should be good enough to distinguish each body structure and detect any health problems under an expert evaluation and/or statistical analysis.

Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix possesses a block-sparse structure, i.e., the non-zero entries occur in clusters or blocks and the number of such non-zero blocks is very small compared to the parameter dimension. Furthermore, a high-dimensional setting is considered where the parameter dimension is quite large compared to the number of available measurements. To perform model selection in this setting, we present an information criterion that is a generalization of the Extended Bayesian Information Criterion-Robust (EBIC-R) and it takes into account both the block structure and the high-dimensionality scenario. We name it Generalized EBIC-R (GEBIC-R). The analytical steps for deriving the GEBIC-R are provided. Simulation results show that the proposed method performs considerably better than the existing state-of-the-art methods and achieves empirical consistency at large sample sizes and/or at high-SNR., Part of ISBN 978-9-4645-9360-0QC 20231124

Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix possesses a block-sparse structure, i.e., the non-zero entries occur in clusters or blocks and the number of such non-zero blocks is very small compared to the parameter dimension. Furthermore, a high-dimensional setting is considered where the parameter dimension is quite large compared to the number of available measurements. To perform model selection in this setting, we present an information criterion that is a generalization of the Extended Bayesian Information Criterion-Robust (EBIC-R) and it takes into account both the block structure and the high-dimensionality scenario. We name it Generalized EBIC-R (GEBIC-R). The analytical steps for deriving the GEBIC-R are provided. Simulation results show that the proposed method performs considerably better than the existing state-of-the-art methods and achieves empirical consistency at large sample sizes and/or at high-SNR., Part of ISBN 978-9-4645-9360-0QC 20231124

Compressive Sensing (CS) has well boosted massive random access protocols over the last decade. Usually, on physical layer, the protocols employ some fat matrix with the property that sparse vectors in the much larger column space domain can still be recovered. This, in turn, greatly reduces the chances of collisions between access devices. This basic scheme has meanwhile been enhanced in various directions but the system cannot operate in overload regime, i.e. sustain significantly more users than the row dimension of the fat matrix dictates. In this paper, we take a different route and apply an orthogonal DFT basis as it is used in OFDM, but subdivide its image into so-called sub-channels and let each sub-channel take only a fraction of the load. In a random fashion the subdivision is consecutively applied over a suitable number of time-slots. Within the time-slots the users will not change their sub-channel assignment and send in parallel the data. Activity detection is carried out jointly across time-slots in each of the sub-channels. For such system design we derive three rather fundamental results: i) First, we prove that the subdivision can be driven to the extent that the activity in each sub-channel is sparse by design. An effect that we call sparsity capture effect . ii) Second, we prove that effectively the system can sustain any overload situation relative to the DFT dimension, i.e. detection failure of active and non-active users can be kept below any desired threshold regardless of the number of users. The only price to pay is delay, i.e. the number of time-slots over which cross-detection is performed. We achieve this by jointly exploring the effect of measure concentration in time and frequency and careful system parameter scaling. iii) Third, we prove that parallel to activity detection active users can carry one symbol per pilot and time-slot so it supports so-called one-shot messaging . The key to proving these results are new concentration result

This work investigates the use of compressed sensing to reduce measurement times in magnetic resonance imaging (MRI) and magnetic particle imaging (MPI). To this end, a flexible yet performant image reconstruction framework is developed. Based on this, an efficient reconstruction scheme for non Cartesian MRI is proposed and a low-rank-based method for the estimation of MPI system matrices is developed. Finally, an experiment design framework is developed to obtain optimized sampling patterns for both MRI and MPI., Diese Arbeit untersucht den Einsatz des Compressed Sensing zur Messzeitreduktion bei der Magnetresonanztomographie (MRT) und Magnetpartikelbildgebung (MPI). Hierzu wird ein flexibles und performantes Bildrekonstruktionsframework entwickelt. Anschließend wird ein effizientes Rekonstruktionsschema für nicht-kartesische MRT und eine verbesserte Methode für die Schätzung von MPI-Systemmatrizen vorgeschlagen. Abschließend wird ein Framework zur Optimierung von Abtastmustern für MRI und MPI vorgestellt.

Reconfigurable intelligent surface (RIS) is an emerging tool for 5G and wireless communication technologies that have attracted researchers' interest. However, the passive nature and the high number of reflecting elements in RIS result in a large pilot overhead, which makes channel estimation challenging in multi-user multiple-input multiple-output (MU-MIMO) wireless communication systems. Previous works have shown an improvement in reducing the pilot overhead by exploiting the structured sparsity in rows and columns, which was further improved by compensating offset among users in angular cascaded channels of RIS aided system. To further reduce the pilot overhead, we analyze and adopt coherence-optimized pilots for channel estimation and propose an algorithm to analyze the combined effect of low-coherence pilots with an optimum size of RIS elements for a given number of users, transmit antennas, and normalized error threshold performance. The simulation results illustrate better NMSE performance as compared to contemporary techniques.

Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix possesses a block-sparse structure, i.e., the non-zero entries occur in clusters or blocks and the number of such non-zero blocks is very small compared to the parameter dimension. Furthermore, a high-dimensional setting is considered where the parameter dimension is quite large compared to the number of available measurements. To perform model selection in this setting, we present an information criterion that is a generalization of the Extended Bayesian Information Criterion-Robust (EBIC-R) and it takes into account both the block structure and the high-dimensionality scenario. We name it Generalized EBIC-R (GEBIC-R). The analytical steps for deriving the GEBIC-R are provided. Simulation results show that the proposed method performs considerably better than the existing state-of-the-art methods and achieves empirical consistency at large sample sizes and/or at high-SNR., Part of ISBN 978-9-4645-9360-0QC 20231124

Reconfigurable intelligent surface (RIS) is an emerging tool for 5G and wireless communication technologies that have attracted researchers' interest. However, the passive nature and the high number of reflecting elements in RIS result in a large pilot overhead, which makes channel estimation challenging in multi-user multiple-input multiple-output (MU-MIMO) wireless communication systems. Previous works have shown an improvement in reducing the pilot overhead by exploiting the structured sparsity in rows and columns, which was further improved by compensating offset among users in angular cascaded channels of RIS aided system. To further reduce the pilot overhead, we analyze and adopt coherence-optimized pilots for channel estimation and propose an algorithm to analyze the combined effect of low-coherence pilots with an optimum size of RIS elements for a given number of users, transmit antennas, and normalized error threshold performance. The simulation results illustrate better NMSE performance as compared to contemporary techniques.

Compressed sensing is a new technique for data acquisition, which reconstructs the original signal from a small number of measurements. The performance of compressed sensing depends on the design of measurement and basis matrices. To improve the reconstruction accuracy, dictionary learning methods have been developed to customize basis matrices for specific signals. However, it may be difficult to obtain the theoretically optimal results because of the restrictions in physical realization such as the sensor placement and accessibility in the working environment. In this paper, a feature-based physics-constrained active dictionary learning (FB-PCADL) framework is proposed to solve the compression and classification problems simultaneously for image-based additive manufacturing process monitoring. A new active dictionary learning strategy is developed to optimize the measurement matrix, where the reconstruction errors are gradually reduced with the new measurements taken adaptively at the positions where the largest reconstruction errors occur. In addition, important features in images are identified and used to enhance the classification accuracy. The FB-PCADL framework is demonstrated with thermal images in monitoring fused filament fabrication process and optical images in monitoring laser powder bed fusion process.

Bayesian modelling of the channel distribution is a crucial step before channel recovery specially in the underdetermined scenario in multiple input multiple output (MIMO) antenna setups. In complicated dynamic propagation environments such as the ones encountered in Unmanned Aerial Vehicles (UAVs) Air to Ground (A2G) channels, Bayesian modelling might not be feasible or the model may not be able to approximate the different aspects of the true distribution well enough. Thus, estimation performance will be affected irrespective of the efficiency of recovery algorithm. To exploit the temporal correlations and imperfections in the real channels in such a scenario, we design a temporally correlated adversarial regulariser using Variational recurrent neural networks (VRNN) and train the framework on simulated channel dataset. The framework can be trained directly with channel samples, thus, allowing channel modelling and estimation without explicit tractable Bayesian models in highly dynamic systems. We then propose a temporally correlated deep compressed sensing algorithm which does not depend on the expressibility of the networks and provide theoretical results for existence and recovery. Numerical experiments demonstrate its effectiveness for channel estimation in A2G channels and show superior channel recovery and improved modelling even for out-of-distribution channels.

Magnetic Resonance Imaging (MRI) offers strong soft tissue contrast but suffers from long acquisition times and requires tedious annotation from radiologists. Traditionally, these challenges have been addressed separately with reconstruction and image analysis algorithms. To see if performance could be improved by treating both as end-to-end, we hosted the K2S challenge, in which challenge participants segmented knee bones and cartilage from 8× undersampled k-space. We curated the 300-patient K2S dataset of multicoil raw k-space and radiologist quality-checked segmentations. 87 teams registered for the challenge and there were 12 submissions, varying in methodologies from serial reconstruction and segmentation to end-to-end networks to another that eschewed a reconstruction algorithm altogether. Four teams produced strong submissions, with the winner having a weighted Dice Similarity Coefficient of 0.910 ± 0.021 across knee bones and cartilage. Interestingly, there was no correlation between reconstruction and segmentation metrics. Further analysis showed the top four submissions were suitable for downstream biomarker analysis, largely preserving cartilage thicknesses and key bone shape features with respect to ground truth. K2S thus showed the value in considering reconstruction and image analysis as end-to-end tasks, as this leaves room for optimization while more realistically reflecting the long-term use case of tools being developed by the MR community.

In computational imaging, inverse problems describe the general process of turning measurements into images using algorithms: images from sound waves in sonar, spin orientations in magnetic resonance imaging, or X-ray absorption in computed tomography.Today, the two dominant algorithmic approaches for solving inverse problems are compressed sensing and deep learning. Compressed sensing leverages convex optimization and comes with strong theoretical guarantees of correct reconstruction, but requires linear measurements and substantial processor memory, both of which limit its applicability to many imaging modalities. In contrast, deep learning methods leverage nonconvex optimization and neural networks, allowing them to use nonlinear measurements and limited memory. However, they can be unreliable, and are difficult to inspect, analyze, and predict when they will produce correct reconstructions. In this dissertation, we focus on an inverse problem central to computer vision and graphics: given calibrated photographs of a scene, recover the optical density and view-dependent color of every point in the scene. For this problem, we take steps to bridge the best aspects of compressed sensing and deep learning: (i) combining an explicit, non-neural scene representation with optimization through a nonlinear forward model, (ii) reducing memory requirements through a compressed representation that retains aspects of interpretability, and extends to dynamic scenes, and (iii) presenting a preliminary convergence analysis that suggests faithful reconstruction under our modeling.

Many real-world scenarios for massive machine-type communication involve sensors monitoring a physical phenomenon. As a consequence, the activity pattern of these sensors will be correlated. In this letter, we study how the correlation of user activities can be exploited to improve detection performance in grant-free random access systems where the users transmit pilot-hopping sequences and the detection is performed based on the received energy. We show that we can expect considerable performance gains by adding regularizers, which take the activity correlation into account, to the non-negative least squares, which has been shown to work well for independent user activity., QC 20230508

Compressive Sensing (CS) has well boosted massive random access protocols over the last decade. Usually, on physical layer, the protocols employ some fat matrix with the property that sparse vectors in the much larger column space domain can still be recovered. This, in turn, greatly reduces the chances of collisions between access devices. This basic scheme has meanwhile been enhanced in various directions but the system cannot operate in overload regime, i.e. sustain significantly more users than the row dimension of the fat matrix dictates. In this paper, we take a different route and apply an orthogonal DFT basis as it is used in OFDM, but subdivide its image into so-called sub-channels and let each sub-channel take only a fraction of the load. In a random fashion the subdivision is consecutively applied over a suitable number of time-slots. Within the time-slots the users will not change their sub-channel assignment and send in parallel the data. Activity detection is carried out jointly across time-slots in each of the sub-channels. For such system design we derive three rather fundamental results: i) First, we prove that the subdivision can be driven to the extent that the activity in each sub-channel is sparse by design. An effect that we call sparsity capture effect . ii) Second, we prove that effectively the system can sustain any overload situation relative to the DFT dimension, i.e. detection failure of active and non-active users can be kept below any desired threshold regardless of the number of users. The only price to pay is delay, i.e. the number of time-slots over which cross-detection is performed. We achieve this by jointly exploring the effect of measure concentration in time and frequency and careful system parameter scaling. iii) Third, we prove that parallel to activity detection active users can carry one symbol per pilot and time-slot so it supports so-called one-shot messaging . The key to proving these results are new concentration result

The THz frequency spectrum provides an opportunity to explore high-resolution synthetic-aperture-radar (SAR) short-range imaging that can be used for various applications. However, the performance of THz SAR imaging is sensitive to phase errors that can be caused by an insufficient amount of data samples for image formation and by path deviations that can be practically caused by SAR platform vibrations, changes in speed, changes in direction, and acceleration. To solve the former problem, an improved interpolation procedure for backprojection algorithms has been proposed. However, to make these algorithms efficient in handling the latter problem, an additional autofocusing is necessary. In this paper, we introduce an autofocusing procedure based on compressed sensing that is incorporated into the backprojection algorithm. The reconstruction is based on the following calculated parameters: windowed interpolation sinc kernel, and range distances between SAR platform and image pixels in a defined image plane. The proposed approach is tested on real data, which was acquired by the 2\pi FMCW SAR system through outdoor SAR imaging. © 2023 IEEE., Multistatic High-resolution Sensing at THz, Project-ID A17

Magnetic resonance imaging (MRI), is a noninvasive medical imaging testing techniquewhich is used to produce detailed images of internal structure of the human body, includingbones, muscles, organs, and blood vessels. MRI scanners use large magnets and radiowaves to create images of the body. Cardiac MRI scan helps doctors to detect and monitorcardiac diseases like blood clots, artery blockages, and scar tissue etc. Cardiovasculardisease is a type of disease that affects the heart or the blood vessels.This thesis aims to explore the reconstruction of accelerated cardiovascular MRI datato reconstruct under-sampled MRI data acquired after applying accelerated techniques.The focus of this research is to study and implement deep learning techniques to overcomethe aliasing artifacts caused by accelerated imaging. The results of this study will becompared with fully sampled data acquired with traditional existing techniques such asParallel Imaging (PI) and Compressed Sensing (CS).The primary findings of this study show that the proposed deep learning network caneffectively reconstruct under-sampled cardiovascular MRI data acquired using acceleratedimaging techniques. Many experiments were performed to handle 4D Flow data with limitedmemory for training the network. The network’s performance was found to be comparableto the fully sampled data acquired using traditional imaging techniques such asPI and CS. It is also important to note that this study also aimed to investigate the generalizabilityof the proposed deep learning network, specifically FlowVN, when appliedto different datasets. To explore this aspect, two different models were employed: a pretrainedmodel using previous research data and configurations, and a model trained fromscratch using CMIV data with experiments performed to address limited memory issuesassociated with 4D Flow data.

The rapid progress with machine learning (ML) technology has solved previously unsolved problems, but training these ML models requires ever larger datasets and increasing amounts of computational resources. One potential solution is to enable parallelization of the computations and allow local processing of training data in distributed nodes, such as Federated Learning (FL). For the implementation of FL over wireless networks, the limitations of communication resources pose constraints on how many information bits can be reliably transmitted, which further affects the accuracy of the aggregated model. Over-the-Air (OtA) computation has recently appeared as an alternative solution for aggregating data over distributed nodes, by exploiting the superposition property of wireless channels. This thesis explores how the linearity of OtA computation and compressed sensing (CS) can be used in combination for update aggregation in an FL system. Particularly, the thesis uses CS with iterative hard thresholding (IHT) as the reconstruction algorithm, and the transmission of a compressed update vector from each node is subject to some total power constraints. Simulation results show that for an OtA FL system with total power constraints, when all nodes have the same (and known) sparsity pattern, applying CS does not bring any obvious benefits as compared to the case of transmitting directly uncompressed sparsified update vectors. However, this conclusion does not rule out the possibility that CS can be an efficient method for OtA FL under different scenarios, e.g., when the sparsity patterns are unknown.

The THz frequency spectrum provides an opportunity to explore high-resolution synthetic-aperture-radar (SAR) short-range imaging that can be used for various applications. However, the performance of THz SAR imaging is sensitive to phase errors that can be caused by an insufficient amount of data samples for image formation and by path deviations that can be practically caused by SAR platform vibrations, changes in speed, changes in direction, and acceleration. To solve the former problem, an improved interpolation procedure for backprojection algorithms has been proposed. However, to make these algorithms efficient in handling the latter problem, an additional autofocusing is necessary. In this paper, we introduce an autofocusing procedure based on compressed sensing that is incorporated into the backprojection algorithm. The reconstruction is based on the following calculated parameters: windowed interpolation sinc kernel, and range distances between SAR platform and image pixels in a defined image plane. The proposed approach is tested on real data, which was acquired by the 2\pi FMCW SAR system through outdoor SAR imaging. © 2023 IEEE., Multistatic High-resolution Sensing at THz, Project-ID A17

Magnetic resonance imaging (MRI), is a noninvasive medical imaging testing techniquewhich is used to produce detailed images of internal structure of the human body, includingbones, muscles, organs, and blood vessels. MRI scanners use large magnets and radiowaves to create images of the body. Cardiac MRI scan helps doctors to detect and monitorcardiac diseases like blood clots, artery blockages, and scar tissue etc. Cardiovasculardisease is a type of disease that affects the heart or the blood vessels.This thesis aims to explore the reconstruction of accelerated cardiovascular MRI datato reconstruct under-sampled MRI data acquired after applying accelerated techniques.The focus of this research is to study and implement deep learning techniques to overcomethe aliasing artifacts caused by accelerated imaging. The results of this study will becompared with fully sampled data acquired with traditional existing techniques such asParallel Imaging (PI) and Compressed Sensing (CS).The primary findings of this study show that the proposed deep learning network caneffectively reconstruct under-sampled cardiovascular MRI data acquired using acceleratedimaging techniques. Many experiments were performed to handle 4D Flow data with limitedmemory for training the network. The network’s performance was found to be comparableto the fully sampled data acquired using traditional imaging techniques such asPI and CS. It is also important to note that this study also aimed to investigate the generalizabilityof the proposed deep learning network, specifically FlowVN, when appliedto different datasets. To explore this aspect, two different models were employed: a pretrainedmodel using previous research data and configurations, and a model trained fromscratch using CMIV data with experiments performed to address limited memory issuesassociated with 4D Flow data.

The compressed sensing (CS) has been demonstrated as a promising solution for low-cost signal acquisition in wireless body area network. In this paper, a novel signal reconstruction scheme based on adaptive dictionary and matched filtering in CS domain is proposed for the ECG acquisition. The proposed method selects adaptive overcomplete dictionary based on the QRS estimation of the compressed measurements in each frame. If a QRS complex is estimated in this frame, an adaptive overcomplete dictionary matching the QRS characteristics of this frame is selected for reconstruction, otherwise, a dictionary trained by segments without QRS complex is selected. The ECG frames whose estimated QRS complexes locate in several consecutive locations, the so-called region width, are considered as one category, and will be reconstructed by one overcomplete dictionary which is trained by similar ECG waves. Extensive experiments have been conducted, and the results well demonstrate the effectiveness for signal reconstruction as well as its advantages over some state-of-the-art algorithms.(c) 2022 Elsevier B.V. All rights reserved.

The THz frequency spectrum provides an opportunity to explore high-resolution synthetic-aperture-radar (SAR) short-range imaging that can be used for various applications. However, the performance of THz SAR imaging is sensitive to phase errors that can be caused by an insufficient amount of data samples for image formation and by path deviations that can be practically caused by SAR platform vibrations, changes in speed, changes in direction, and acceleration. To solve the former problem, an improved interpolation procedure for backprojection algorithms has been proposed. However, to make these algorithms efficient in handling the latter problem, an additional autofocusing is necessary. In this paper, we introduce an autofocusing procedure based on compressed sensing that is incorporated into the backprojection algorithm. The reconstruction is based on the following calculated parameters: windowed interpolation sinc kernel, and range distances between SAR platform and image pixels in a defined image plane. The proposed approach is tested on real data, which was acquired by the 2\pi FMCW SAR system through outdoor SAR imaging. © 2023 IEEE., Multistatic High-resolution Sensing at THz, Project-ID A17

The THz frequency spectrum provides an opportunity to explore high-resolution synthetic-aperture-radar (SAR) short-range imaging that can be used for various applications. However, the performance of THz SAR imaging is sensitive to phase errors that can be caused by an insufficient amount of data samples for image formation and by path deviations that can be practically caused by SAR platform vibrations, changes in speed, changes in direction, and acceleration. To solve the former problem, an improved interpolation procedure for backprojection algorithms has been proposed. However, to make these algorithms efficient in handling the latter problem, an additional autofocusing is necessary. In this paper, we introduce an autofocusing procedure based on compressed sensing that is incorporated into the backprojection algorithm. The reconstruction is based on the following calculated parameters: windowed interpolation sinc kernel, and range distances between SAR platform and image pixels in a defined image plane. The proposed approach is tested on real data, which was acquired by the 2\pi FMCW SAR system through outdoor SAR imaging. © 2023 IEEE., Multistatic High-resolution Sensing at THz, Project-ID A17

The THz frequency spectrum provides an opportunity to explore high-resolution synthetic-aperture-radar (SAR) short-range imaging that can be used for various applications. However, the performance of THz SAR imaging is sensitive to phase errors that can be caused by an insufficient amount of data samples for image formation and by path deviations that can be practically caused by SAR platform vibrations, changes in speed, changes in direction, and acceleration. To solve the former problem, an improved interpolation procedure for backprojection algorithms has been proposed. However, to make these algorithms efficient in handling the latter problem, an additional autofocusing is necessary. In this paper, we introduce an autofocusing procedure based on compressed sensing that is incorporated into the backprojection algorithm. The reconstruction is based on the following calculated parameters: windowed interpolation sinc kernel, and range distances between SAR platform and image pixels in a defined image plane. The proposed approach is tested on real data, which was acquired by the 2\pi FMCW SAR system through outdoor SAR imaging. © 2023 IEEE., Multistatic High-resolution Sensing at THz, Project-ID A17

The THz frequency spectrum provides an opportunity to explore high-resolution synthetic-aperture-radar (SAR) short-range imaging that can be used for various applications. However, the performance of THz SAR imaging is sensitive to phase errors that can be caused by an insufficient amount of data samples for image formation and by path deviations that can be practically caused by SAR platform vibrations, changes in speed, changes in direction, and acceleration. To solve the former problem, an improved interpolation procedure for backprojection algorithms has been proposed. However, to make these algorithms efficient in handling the latter problem, an additional autofocusing is necessary. In this paper, we introduce an autofocusing procedure based on compressed sensing that is incorporated into the backprojection algorithm. The reconstruction is based on the following calculated parameters: windowed interpolation sinc kernel, and range distances between SAR platform and image pixels in a defined image plane. The proposed approach is tested on real data, which was acquired by the 2\pi FMCW SAR system through outdoor SAR imaging. © 2023 IEEE., Multistatic High-resolution Sensing at THz, Project-ID A17

Arguably one of the most notable forms of the principle of parsimony was formulated by the philosopher and theologian William of Ockham in the 14th century, and later became well known as Ockham’s Razor principle, which can be phrased as: “Entities should not be multiplied without necessity.” This principle is undoubtedly one of the most fundamental ideas that pervade many branches of knowledge, from philosophy to art and science, from ancient times to modern age, then summarized in the expression “Make everything as simple as possible, but not simpler” as likewise asserted by Albert Einstein. The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In statistics the many applications of sparse modeling span regression, classification tasks, graphical model selection, sparse M-estimators, and sparse dimensionality reduction. It is also particularly effective in many statistical and machine learning areas where the primary goal is to discover predictive patterns from data, which would enhance our understanding and control of underlying physical, biological, and other natural processes, beyond just building accurate outcome black-box predictors. Common examples include selecting biomarkers in biological procedures, finding relevant brain activity locations, which are predictive about brain states and processes based on fMRI data, and identifying network bottlenecks best explaining end-to-end performance. Moreover, the research and applications of efficient recovery of high-dimensional sparse signals from a relatively small number of observations, which is the main focus of compressed sensing or compressive sensing, have rapidly grown and became an extremely intense area of study beyond classical signal processing. Likewise interestingly, sparse modeling is directly related to various artificial visi

Photo-realistic rendering and predictive image synthesis are becoming increasingly important and utilized in many application areas ranging from production of visual effects and product visualization to digital design and the generation of synthetic data for visual machine learning applications. Many essential components of the realistic image synthesis pipelines have been developed tremendously over the last decades. One key component is accurate measurement, modeling, and simulation of how a surface material scatters light. The scattering of light at a point on a surface (reflectance and color) is described by the Bidirectional Reflectance Distribution Function (BRDF); which is the main research topic of this thesis. The BRDF describes how radiance, light, incident at a point on a surface is scattered towards any view-point from which the surface is observed. Accurate acquisition and representation of material properties play a fundamental role in photo-realistic image synthesis, and form a highly interesting research topic with many applications. The thesis has explored and studied appearance modeling, sparse representation and sparse acquisition of BRDFs. The topics of this thesis cover two main areas. Within the first area, BRDF modeling, we propose several new BRDF models for accurate representation of material scattering behaviour using simple but efficient methods. The research challenges in BRDF modeling include tensor decomposition methods and sparse approximations based on measured BRDF data. The second part of the contributions focuses on sparse BRDF sampling and novel highly efficient BRDF acquisition. The sparse BRDF sampling is to tackle tedious and time-consuming processes for acquiring BRDFs. This challenging problem is addressed using sparse modeling and compressed sensing techniques and enables a BRDF to be measured and accurately reconstructed using only a small number of samples. Additionally, the thesis provides example applications based on t, Fotorealistisk rendering och prediktiv bildsyntes har blivit allt viktigare och an-vänds i flera olika tillämpningsområden, allt ifrån produktion av visuella effekter och produktvisualisering till digital design och generering av syntetiska data för tillämpningar inom visuell maskininlärning. Utvecklingen har tagit en ordentlig fart under de senaste decennierna för många av de väsentliga komponenterna i det fotorealistiska bildsyntes-området. En nyckelkomponent inom området är att noggrant kunna mäta, modellera och simulera ljusets spridning från ytan hos ett material. Ljusspridningen från en punkt på en yta med reflektion och färg, beskrivs av en funktion (eng. BRDF); vilket är det huvudsakliga forskningsområdet i den här avhandlingen. BRDF beskriver hur strålning, ljus i detta fall, träffar en punkt på en yta och sprids mot varje observerad synvinkel. En noggrann uppmätning och representation av materialegenskaper är en fundamental del i fotorealistisk bildsyntes och omger ett väldigt intressant forskningsområde med många tillämpningar. Den här avhandlingen har utforskat och studerat modellering för materialytors utseende, glesa representationer och glesa mätningar av ljusspridningsfunktioner. Avhandlingen täcker två huvudområden. Inom det första området, BRDF-modellering, så presenterar vi ett flertal nya BRDF-modeller för noggrann representation av ljusspridningens beteende från materialets yta genom att använda simpla men effektiva metoder. Forskningsutmaningarna inom BRDF-modellering inkluderar både metoder för tensoruppdelning och glesa approximationer baserat på uppmätt BRDF-data. Den andra delen fokuserar på gles BRDF-sampling och en ny och effektiv mätningsmetod för att mäta BRDF. Syftet med den glesa BRDF-samplingen är för att förenkla och snabba upp de enormt tidskrävande processerna som krävs för att mäta BRDF. Detta utmanande problem löses genom att använda glesa modeller och tekniker från compressed sensing som möjliggör att BRDF kan be uppmätt och no

Regular maintenance of civil engineering structures is essential for their safety. Current maintenance regimes involve periodic inspections at regular time intervals. In the time between inspections, there can be a critical development in the structural integrity of a structure, which can be expensive to repair or could even lead to structural failure. A more robust maintenance approach would involve continuous monitoring of the structure. This is the research area of Structural Health Monitoring (SHM). Vibration-based monitoring, which is a subset of SHM, aims to provide new cost-effective maintenance solutions that provide long-term life-safety benefits. Vibration-based monitoring uses vibration measurements from sensors to assess the "Health" of a structure. Damage in a structure will alter the structure's stiffness, mass and damping characteristics, which in turn will change the dynamic properties of the system. This change can then be discovered in the vibration data. The growth of the field is partly due to the significant advances in data-driven science and engineering in recent decades. One of the issues in vibration-based monitoring is the presence of operational and environmental variability in the vibration data. With this variability present, it is challenging to determine from vibration data the characteristics of the underlying dynamic system. The aim of this thesis is to use Robust Principal Component Analysis (rPCA) to reduce or eliminate the operational variability from the traffic to allow for environmental and damage detection. rPCA is a matrix factorisation method that decomposes a data matrix into a low-rank matrix L and a sparse matrix S. The reconstructed low-rank matrix L contains the main correlations in the data that are robust to outliers and corrupt data that are contained in the sparse matrix S. By applying rPCA to the frequency representation of the vibration data, it is hoped that the underlying coherent structure correspondi, Civil Engineering

The rapid progress with machine learning (ML) technology has solved previously unsolved problems, but training these ML models requires ever larger datasets and increasing amounts of computational resources. One potential solution is to enable parallelization of the computations and allow local processing of training data in distributed nodes, such as Federated Learning (FL). For the implementation of FL over wireless networks, the limitations of communication resources pose constraints on how many information bits can be reliably transmitted, which further affects the accuracy of the aggregated model. Over-the-Air (OtA) computation has recently appeared as an alternative solution for aggregating data over distributed nodes, by exploiting the superposition property of wireless channels. This thesis explores how the linearity of OtA computation and compressed sensing (CS) can be used in combination for update aggregation in an FL system. Particularly, the thesis uses CS with iterative hard thresholding (IHT) as the reconstruction algorithm, and the transmission of a compressed update vector from each node is subject to some total power constraints. Simulation results show that for an OtA FL system with total power constraints, when all nodes have the same (and known) sparsity pattern, applying CS does not bring any obvious benefits as compared to the case of transmitting directly uncompressed sparsified update vectors. However, this conclusion does not rule out the possibility that CS can be an efficient method for OtA FL under different scenarios, e.g., when the sparsity patterns are unknown.

(1) Background: Radial RARE-EPI MRI facilitates simultaneous T2 and T2* mapping (2in1-RARE-EPI). With modest undersampling (R = 2), the speed gain of 2in1-RARE-EPI relative to Multi-Spin-Echo and Multi-Gradient-Recalled-Echo references is limited. Further reduction in scan time is crucial for clinical studies investigating T2 and T2* as imaging biomarkers. We demonstrate the feasibility of further acceleration, utilizing compressed sensing (CS) reconstruction of highly undersampled 2in1-RARE-EPI. (2) Methods: Two-fold radially-undersampled 2in1-RARE-EPI data from phantoms, healthy volunteers (n = 3), and multiple sclerosis patients (n = 4) were used as references, and undersampled (Rextra = 1–12, effective undersampling Reff = 2–24). For each echo time, images were reconstructed using CS-reconstruction. For T2 (RARE module) and T2* mapping (EPI module), a linear least-square fit was applied to the images. T2 and T2* from CS-reconstruction of undersampled data were benchmarked against values from CS-reconstruction of the reference data. (3) Results: We demonstrate accelerated simultaneous T2 and T2* mapping using undersampled 2in1-RARE-EPI with CS-reconstruction is feasible. For Rextra = 6 (TA = 01:39 min), the overall MAPE was ≤8% (T2*) and ≤4% (T2); for Rextra = 12 (TA = 01:06 min), the overall MAPE was <13% (T2*) and <5% (T2). (4) Conclusion: Substantial reductions in scan time are achievable for simultaneous T2 and T2* mapping of the brain using highly undersampled 2in1-RARE-EPI with CS-reconstruction., European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program, Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany, Peer Reviewed

Photo-realistic rendering and predictive image synthesis are becoming increasingly important and utilized in many application areas ranging from production of visual effects and product visualization to digital design and the generation of synthetic data for visual machine learning applications. Many essential components of the realistic image synthesis pipelines have been developed tremendously over the last decades. One key component is accurate measurement, modeling, and simulation of how a surface material scatters light. The scattering of light at a point on a surface (reflectance and color) is described by the Bidirectional Reflectance Distribution Function (BRDF); which is the main research topic of this thesis. The BRDF describes how radiance, light, incident at a point on a surface is scattered towards any view-point from which the surface is observed. Accurate acquisition and representation of material properties play a fundamental role in photo-realistic image synthesis, and form a highly interesting research topic with many applications. The thesis has explored and studied appearance modeling, sparse representation and sparse acquisition of BRDFs. The topics of this thesis cover two main areas. Within the first area, BRDF modeling, we propose several new BRDF models for accurate representation of material scattering behaviour using simple but efficient methods. The research challenges in BRDF modeling include tensor decomposition methods and sparse approximations based on measured BRDF data. The second part of the contributions focuses on sparse BRDF sampling and novel highly efficient BRDF acquisition. The sparse BRDF sampling is to tackle tedious and time-consuming processes for acquiring BRDFs. This challenging problem is addressed using sparse modeling and compressed sensing techniques and enables a BRDF to be measured and accurately reconstructed using only a small number of samples. Additionally, the thesis provides example applications based on t, Fotorealistisk rendering och prediktiv bildsyntes har blivit allt viktigare och an-vänds i flera olika tillämpningsområden, allt ifrån produktion av visuella effekter och produktvisualisering till digital design och generering av syntetiska data för tillämpningar inom visuell maskininlärning. Utvecklingen har tagit en ordentlig fart under de senaste decennierna för många av de väsentliga komponenterna i det fotorealistiska bildsyntes-området. En nyckelkomponent inom området är att noggrant kunna mäta, modellera och simulera ljusets spridning från ytan hos ett material. Ljusspridningen från en punkt på en yta med reflektion och färg, beskrivs av en funktion (eng. BRDF); vilket är det huvudsakliga forskningsområdet i den här avhandlingen. BRDF beskriver hur strålning, ljus i detta fall, träffar en punkt på en yta och sprids mot varje observerad synvinkel. En noggrann uppmätning och representation av materialegenskaper är en fundamental del i fotorealistisk bildsyntes och omger ett väldigt intressant forskningsområde med många tillämpningar. Den här avhandlingen har utforskat och studerat modellering för materialytors utseende, glesa representationer och glesa mätningar av ljusspridningsfunktioner. Avhandlingen täcker två huvudområden. Inom det första området, BRDF-modellering, så presenterar vi ett flertal nya BRDF-modeller för noggrann representation av ljusspridningens beteende från materialets yta genom att använda simpla men effektiva metoder. Forskningsutmaningarna inom BRDF-modellering inkluderar både metoder för tensoruppdelning och glesa approximationer baserat på uppmätt BRDF-data. Den andra delen fokuserar på gles BRDF-sampling och en ny och effektiv mätningsmetod för att mäta BRDF. Syftet med den glesa BRDF-samplingen är för att förenkla och snabba upp de enormt tidskrävande processerna som krävs för att mäta BRDF. Detta utmanande problem löses genom att använda glesa modeller och tekniker från compressed sensing som möjliggör att BRDF kan be uppmätt och no

Photo-realistic rendering and predictive image synthesis are becoming increasingly important and utilized in many application areas ranging from production of visual effects and product visualization to digital design and the generation of synthetic data for visual machine learning applications. Many essential components of the realistic image synthesis pipelines have been developed tremendously over the last decades. One key component is accurate measurement, modeling, and simulation of how a surface material scatters light. The scattering of light at a point on a surface (reflectance and color) is described by the Bidirectional Reflectance Distribution Function (BRDF); which is the main research topic of this thesis. The BRDF describes how radiance, light, incident at a point on a surface is scattered towards any view-point from which the surface is observed. Accurate acquisition and representation of material properties play a fundamental role in photo-realistic image synthesis, and form a highly interesting research topic with many applications. The thesis has explored and studied appearance modeling, sparse representation and sparse acquisition of BRDFs. The topics of this thesis cover two main areas. Within the first area, BRDF modeling, we propose several new BRDF models for accurate representation of material scattering behaviour using simple but efficient methods. The research challenges in BRDF modeling include tensor decomposition methods and sparse approximations based on measured BRDF data. The second part of the contributions focuses on sparse BRDF sampling and novel highly efficient BRDF acquisition. The sparse BRDF sampling is to tackle tedious and time-consuming processes for acquiring BRDFs. This challenging problem is addressed using sparse modeling and compressed sensing techniques and enables a BRDF to be measured and accurately reconstructed using only a small number of samples. Additionally, the thesis provides example applications based on t, Fotorealistisk rendering och prediktiv bildsyntes har blivit allt viktigare och an-vänds i flera olika tillämpningsområden, allt ifrån produktion av visuella effekter och produktvisualisering till digital design och generering av syntetiska data för tillämpningar inom visuell maskininlärning. Utvecklingen har tagit en ordentlig fart under de senaste decennierna för många av de väsentliga komponenterna i det fotorealistiska bildsyntes-området. En nyckelkomponent inom området är att noggrant kunna mäta, modellera och simulera ljusets spridning från ytan hos ett material. Ljusspridningen från en punkt på en yta med reflektion och färg, beskrivs av en funktion (eng. BRDF); vilket är det huvudsakliga forskningsområdet i den här avhandlingen. BRDF beskriver hur strålning, ljus i detta fall, träffar en punkt på en yta och sprids mot varje observerad synvinkel. En noggrann uppmätning och representation av materialegenskaper är en fundamental del i fotorealistisk bildsyntes och omger ett väldigt intressant forskningsområde med många tillämpningar. Den här avhandlingen har utforskat och studerat modellering för materialytors utseende, glesa representationer och glesa mätningar av ljusspridningsfunktioner. Avhandlingen täcker två huvudområden. Inom det första området, BRDF-modellering, så presenterar vi ett flertal nya BRDF-modeller för noggrann representation av ljusspridningens beteende från materialets yta genom att använda simpla men effektiva metoder. Forskningsutmaningarna inom BRDF-modellering inkluderar både metoder för tensoruppdelning och glesa approximationer baserat på uppmätt BRDF-data. Den andra delen fokuserar på gles BRDF-sampling och en ny och effektiv mätningsmetod för att mäta BRDF. Syftet med den glesa BRDF-samplingen är för att förenkla och snabba upp de enormt tidskrävande processerna som krävs för att mäta BRDF. Detta utmanande problem löses genom att använda glesa modeller och tekniker från compressed sensing som möjliggör att BRDF kan be uppmätt och no

Photo-realistic rendering and predictive image synthesis are becoming increasingly important and utilized in many application areas ranging from production of visual effects and product visualization to digital design and the generation of synthetic data for visual machine learning applications. Many essential components of the realistic image synthesis pipelines have been developed tremendously over the last decades. One key component is accurate measurement, modeling, and simulation of how a surface material scatters light. The scattering of light at a point on a surface (reflectance and color) is described by the Bidirectional Reflectance Distribution Function (BRDF); which is the main research topic of this thesis. The BRDF describes how radiance, light, incident at a point on a surface is scattered towards any view-point from which the surface is observed. Accurate acquisition and representation of material properties play a fundamental role in photo-realistic image synthesis, and form a highly interesting research topic with many applications. The thesis has explored and studied appearance modeling, sparse representation and sparse acquisition of BRDFs. The topics of this thesis cover two main areas. Within the first area, BRDF modeling, we propose several new BRDF models for accurate representation of material scattering behaviour using simple but efficient methods. The research challenges in BRDF modeling include tensor decomposition methods and sparse approximations based on measured BRDF data. The second part of the contributions focuses on sparse BRDF sampling and novel highly efficient BRDF acquisition. The sparse BRDF sampling is to tackle tedious and time-consuming processes for acquiring BRDFs. This challenging problem is addressed using sparse modeling and compressed sensing techniques and enables a BRDF to be measured and accurately reconstructed using only a small number of samples. Additionally, the thesis provides example applications based on t, Fotorealistisk rendering och prediktiv bildsyntes har blivit allt viktigare och an-vänds i flera olika tillämpningsområden, allt ifrån produktion av visuella effekter och produktvisualisering till digital design och generering av syntetiska data för tillämpningar inom visuell maskininlärning. Utvecklingen har tagit en ordentlig fart under de senaste decennierna för många av de väsentliga komponenterna i det fotorealistiska bildsyntes-området. En nyckelkomponent inom området är att noggrant kunna mäta, modellera och simulera ljusets spridning från ytan hos ett material. Ljusspridningen från en punkt på en yta med reflektion och färg, beskrivs av en funktion (eng. BRDF); vilket är det huvudsakliga forskningsområdet i den här avhandlingen. BRDF beskriver hur strålning, ljus i detta fall, träffar en punkt på en yta och sprids mot varje observerad synvinkel. En noggrann uppmätning och representation av materialegenskaper är en fundamental del i fotorealistisk bildsyntes och omger ett väldigt intressant forskningsområde med många tillämpningar. Den här avhandlingen har utforskat och studerat modellering för materialytors utseende, glesa representationer och glesa mätningar av ljusspridningsfunktioner. Avhandlingen täcker två huvudområden. Inom det första området, BRDF-modellering, så presenterar vi ett flertal nya BRDF-modeller för noggrann representation av ljusspridningens beteende från materialets yta genom att använda simpla men effektiva metoder. Forskningsutmaningarna inom BRDF-modellering inkluderar både metoder för tensoruppdelning och glesa approximationer baserat på uppmätt BRDF-data. Den andra delen fokuserar på gles BRDF-sampling och en ny och effektiv mätningsmetod för att mäta BRDF. Syftet med den glesa BRDF-samplingen är för att förenkla och snabba upp de enormt tidskrävande processerna som krävs för att mäta BRDF. Detta utmanande problem löses genom att använda glesa modeller och tekniker från compressed sensing som möjliggör att BRDF kan be uppmätt och no

Photo-realistic rendering and predictive image synthesis are becoming increasingly important and utilized in many application areas ranging from production of visual effects and product visualization to digital design and the generation of synthetic data for visual machine learning applications. Many essential components of the realistic image synthesis pipelines have been developed tremendously over the last decades. One key component is accurate measurement, modeling, and simulation of how a surface material scatters light. The scattering of light at a point on a surface (reflectance and color) is described by the Bidirectional Reflectance Distribution Function (BRDF); which is the main research topic of this thesis. The BRDF describes how radiance, light, incident at a point on a surface is scattered towards any view-point from which the surface is observed. Accurate acquisition and representation of material properties play a fundamental role in photo-realistic image synthesis, and form a highly interesting research topic with many applications. The thesis has explored and studied appearance modeling, sparse representation and sparse acquisition of BRDFs. The topics of this thesis cover two main areas. Within the first area, BRDF modeling, we propose several new BRDF models for accurate representation of material scattering behaviour using simple but efficient methods. The research challenges in BRDF modeling include tensor decomposition methods and sparse approximations based on measured BRDF data. The second part of the contributions focuses on sparse BRDF sampling and novel highly efficient BRDF acquisition. The sparse BRDF sampling is to tackle tedious and time-consuming processes for acquiring BRDFs. This challenging problem is addressed using sparse modeling and compressed sensing techniques and enables a BRDF to be measured and accurately reconstructed using only a small number of samples. Additionally, the thesis provides example applications based on t, Fotorealistisk rendering och prediktiv bildsyntes har blivit allt viktigare och an-vänds i flera olika tillämpningsområden, allt ifrån produktion av visuella effekter och produktvisualisering till digital design och generering av syntetiska data för tillämpningar inom visuell maskininlärning. Utvecklingen har tagit en ordentlig fart under de senaste decennierna för många av de väsentliga komponenterna i det fotorealistiska bildsyntes-området. En nyckelkomponent inom området är att noggrant kunna mäta, modellera och simulera ljusets spridning från ytan hos ett material. Ljusspridningen från en punkt på en yta med reflektion och färg, beskrivs av en funktion (eng. BRDF); vilket är det huvudsakliga forskningsområdet i den här avhandlingen. BRDF beskriver hur strålning, ljus i detta fall, träffar en punkt på en yta och sprids mot varje observerad synvinkel. En noggrann uppmätning och representation av materialegenskaper är en fundamental del i fotorealistisk bildsyntes och omger ett väldigt intressant forskningsområde med många tillämpningar. Den här avhandlingen har utforskat och studerat modellering för materialytors utseende, glesa representationer och glesa mätningar av ljusspridningsfunktioner. Avhandlingen täcker två huvudområden. Inom det första området, BRDF-modellering, så presenterar vi ett flertal nya BRDF-modeller för noggrann representation av ljusspridningens beteende från materialets yta genom att använda simpla men effektiva metoder. Forskningsutmaningarna inom BRDF-modellering inkluderar både metoder för tensoruppdelning och glesa approximationer baserat på uppmätt BRDF-data. Den andra delen fokuserar på gles BRDF-sampling och en ny och effektiv mätningsmetod för att mäta BRDF. Syftet med den glesa BRDF-samplingen är för att förenkla och snabba upp de enormt tidskrävande processerna som krävs för att mäta BRDF. Detta utmanande problem löses genom att använda glesa modeller och tekniker från compressed sensing som möjliggör att BRDF kan be uppmätt och no

Purpose: To assess the cervical magnetic resonance neurography (MRN) imaging quality obtained with compressed sensing and sensitivity-encoding (compressed SENSE; CS-SENSE) technique in comparison to that obtained with the conventional parallel imaging (i.e., SENSE) technique. Materials and methods: Five healthy volunteers underwent a three-dimensional (3D) turbo spin-echo (TSE)-based cervical MRN examination using a 3.0 Tesla MR-unit. All MRN acquisitions were performed with CS-SENSE and conventional SENSE. We used four acceleration factors (4, 8, 16 and 32) in CS-SENSE. The image quality in MRN was evaluated by assessing the degree of cervical nerve depiction using the contrast ratio (CR) and contrast-noise ratio (CNR) between the cervical nerve and the background signal intensity and a visual scoring system (1: poor, 2: moderate, 3: good). In all of the CR, CNR and visual score, we calculated the ratio of the CS-SENSE-based MRN to that from SENSE-based MRN plus the 95% confidence intervals (CIs) of these ratios. Results: In the multiple comparison of MRN images with the control of conventional SENSE-based MRN, both the quantitative CR values and the visual score for the CS-SENSE factors of 16 and 32 were significantly lower, whereas the CS-SENSE factors of 4 and 8 showed a non-significant difference. In addition, the quantitative CNR values obtained with the CS-SENSE factors of 4 and 8 were significantly higher than that obtained with the conventional SENSE-based MRN while the CS-SENSE factor of 32 was significantly lower, in contrast, the CS SENSE factors of 16 showed a non-significant difference. For CS-SENSE factors of 4 and 8, all ratios of the CS SENSE-based MRN values for CR, CNR and visual scores to those from SENSE-based MRN were above 0.95. Conclusion: CS-SENSE-based MRN can accomplish fast scanning with sufficient image quality when using a high acceleration factor.

Mit ständig wachsenden Datenmengen wird die Aufgabe, zugrunde liegende Struktur zu finden und zu nutzen, immer wichtiger. Eine einflussreiche Erkenntnis, auf die sich moderne Signalverarbeitung wie Compressed Sensing oder Dictionary Learning stützen, ist, dass viele Datentypen eine Art von sparser Darstellung erlauben. Für eine geeignete Basis reicht also eine kleine Anzahl von Elementen aus, um ein beliebiges Signal zu approximieren. Im ersten Teil dieser Arbeit leiten wir technische Ergebnisse her, die es uns ermöglichen, Compressed Sensing und Dictionary Learning in allgemeineren Zusammenhängen zu analysieren, als dies bisher möglich war. Konkret leiten wir Konzentrationsungleichungen für die Operatornorm von zufälligen Submatrizen mit ungleichmäßig verteilten Trägern ab, wobei wir im Wesentlichen zeigen, dass sich die meisten Submatrizen einer gut konditionierten Matrix wie Isometrien verhalten. Bei Compressed Sensing wird ein sparses Signal aus einer möglichst kleinen Anzahl von linearen Messungen rekonstruiert. Wenn diese Messungen aus einer größeren Menge möglicher linearer Messungen durch sampling von einer (möglicherweise ungleichmäßigen) Wahrscheinlichkeitsdichte ausgewählt werden, nennt man dies subsampling (variable density subsampling). Im nächsten Teil der Arbeit leiten wir eine optimale Dichte her, die die Wiederherstellung in einem sehr allgemeinen Setting garantiert. Genauer gesagt zeigen wir, wie die optimale Dichte von der Struktur der Messmatrix und von der Verteilung der sparsen Trägern abhängt, die leicht aus den Daten geschätzt werden können. Dies führt zu einer einfachen Formel für Dichten, die in numerischen Experimenten den neuesten Stand der Technik erreichen. Unser Ansatz lässt sich auch auf strukturierte Erfassungen ausdehnen, bei denen anstelle von Einzelmessungen Blöcke von Messungen vorgenommen werden. In einigen Anwendungen ist die sparsifizierende Basis nicht bekannt oder man möchte eine bessere Basis finden. Das Erlernen einer solc, With ever growing amounts of data, the task of finding and using underlying structure is be- coming more and more important. One influential insight, which modern signal processing tasks like compressed sensing or dictionary learning rely on, is that many data types allow some kind of sparse representation. So given a suitable basis, a small number of elements is sufficient to approximate any given signal. In the first part of this thesis we derive technical results allowing us to analyse compressed sensing and dictionary learning in more general settings than previously possible. Concretely, we derive tail bounds for the operator norm of random submatrices with non-uniformly distributed supports, essentially showing that for a well-conditioned matrix most submatrices behave like an isometry. Compressed sensing consists of reconstructing a sparse signal from a small number of linear measurements. If these measurements are chosen from a bigger set of possible linear measurements via sampling from a (possibly non-uniform) probability distribution, this is called (variable density) subsampling. In the next part of the thesis we derive an optimal subsampling density, guaranteeing recovery in a very general setting. More precisely, we show how the optimal subsampling density depends on the structure of the sensing matrix and on the distribution of the sparse supports, which can easily be estimated from data. This leads to a simple formula for subsampling densities achieving state of the art performance in numerical experiments. Our approach also extends to structured acquisition, where instead of isolated measurements, blocks of measurements are taken. In some applications the sparsifying basis is not known or one wants to find a better one. Learning such a basis from data is called dictionary learning. In the third part of this thesis we study the convergence behaviour of two of the most popular dictionary learning algorithms - the Method of Optimal Directions (MOD) and, submitted by Simon Ruetz, Kumulative Dissertation aus zwei Artikeln, Dissertation University of Innsbruck 2022

Purpose: To assess the cervical magnetic resonance neurography (MRN) imaging quality obtained with compressed sensing and sensitivity-encoding (compressed SENSE; CS-SENSE) technique in comparison to that obtained with the conventional parallel imaging (i.e., SENSE) technique. Materials and methods: Five healthy volunteers underwent a three-dimensional (3D) turbo spin-echo (TSE)-based cervical MRN examination using a 3.0 Tesla MR-unit. All MRN acquisitions were performed with CS-SENSE and conventional SENSE. We used four acceleration factors (4, 8, 16 and 32) in CS-SENSE. The image quality in MRN was evaluated by assessing the degree of cervical nerve depiction using the contrast ratio (CR) and contrast-noise ratio (CNR) between the cervical nerve and the background signal intensity and a visual scoring system (1: poor, 2: moderate, 3: good). In all of the CR, CNR and visual score, we calculated the ratio of the CS-SENSE-based MRN to that from SENSE-based MRN plus the 95% confidence intervals (CIs) of these ratios. Results: In the multiple comparison of MRN images with the control of conventional SENSE-based MRN, both the quantitative CR values and the visual score for the CS-SENSE factors of 16 and 32 were significantly lower, whereas the CS-SENSE factors of 4 and 8 showed a non-significant difference. In addition, the quantitative CNR values obtained with the CS-SENSE factors of 4 and 8 were significantly higher than that obtained with the conventional SENSE-based MRN while the CS-SENSE factor of 32 was significantly lower, in contrast, the CS SENSE factors of 16 showed a non-significant difference. For CS-SENSE factors of 4 and 8, all ratios of the CS SENSE-based MRN values for CR, CNR and visual scores to those from SENSE-based MRN were above 0.95. Conclusion: CS-SENSE-based MRN can accomplish fast scanning with sufficient image quality when using a high acceleration factor.

This paper proposes an algorithm to localize a magnetic dipole using a limited number of noisy measurements from magnetic field sensors. The algorithm is based on the theory of compressed sensing, and exploits the sparseness of the magnetic dipole in space. Beforehand, a basis consisting of magnetic dipole fields belonging to individual dipoles in an evenly spaced 3D grid within a specified search domain is constructed. In the algorithm, a number of sensors is chosen which measure all three magnetic field components. The sensors are chosen optimally using QR pivoting. Using the pre-constructed basis and the obtained field measurements, a sparse representation in the location domain is computed using $\ell _{{1}}$ optimization. Based on the resulting sparse representation, the location and magnetic moment of the magnetic dipole are estimated. An extension to an iterative method is implemented, where the basis and chosen sensors improve after every location estimate. Numerical simulations have been performed to verify the algorithm, and experiments have been done for validation. The proposed algorithm is shown to be effective in localizing magnetic dipoles., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Mathematical Physics

Au cours des vingt dernières années, l'imagerie térahertz basée sur la spectroscopie dans le domaine temporel provoque un intérêt croissant grâce à ses capacités particulières d’étudier les caractéristiques spectrales des produits chimiques, d’extraire l'indice de réfraction et l'absorption des matériaux, ainsi que de révéler la structure interne d’objets complexes. Cependant, son utilisation répandue a été entravée par le temps d'acquisition chronophage généralement nécessaire pour balayer spatialement l'objet et, pour chaque point spatial, enregistrer le champ dans le domaine temporel via une ligne à retard. Dans ce projet de recherche, nous avons abordé cet obstacle fondamental en utilisant deux approches complémentaires. Tout d'abord, nous avons mis en œuvre une configuration d'imagerie à « pixel unique » dans le domaine temporel, qui permet d'éviter le balayage spatial et d'utiliser une reconstruction de détection compressée. Nous avons démontré l'extraction cohérente des formes d'onde temporelles térahertz d’une façon indirecte, à chaque position spatiale d'un objet via l’imagerie à « pixel unique ». Cette stratégie permet ainsi de préserver les capacités de sonder les propriétés des matériaux, offertes par la spectroscopie dans le domaine temporel, tout en permettant une réduction du temps d'acquisition. Dans la deuxième partie, nous avons davantage amélioré l'arrangement d'imagerie en utilisant un schéma de détection sans balayage. En exploitant correctement la diffraction naturelle des ondes, un cartographie tempsespace appliquée à la détection de point térahertz permet une acquisition quasi instantanée des formes d'onde térahertz. La combinaison de ces deux approches permet une réduction significative de la complexité du système et du temps d'acquisition, et constitue ainsi une solution prometteuse pour le développement d'imageurs térahertz rapides et compacts de nouvelle génération. In the last twenty years, terahertz imaging based on time-dom

Purpose: To assess the cervical magnetic resonance neurography (MRN) imaging quality obtained with compressed sensing and sensitivity-encoding (compressed SENSE; CS-SENSE) technique in comparison to that obtained with the conventional parallel imaging (i.e., SENSE) technique. Materials and methods: Five healthy volunteers underwent a three-dimensional (3D) turbo spin-echo (TSE)-based cervical MRN examination using a 3.0 Tesla MR-unit. All MRN acquisitions were performed with CS-SENSE and conventional SENSE. We used four acceleration factors (4, 8, 16 and 32) in CS-SENSE. The image quality in MRN was evaluated by assessing the degree of cervical nerve depiction using the contrast ratio (CR) and contrast-noise ratio (CNR) between the cervical nerve and the background signal intensity and a visual scoring system (1: poor, 2: moderate, 3: good). In all of the CR, CNR and visual score, we calculated the ratio of the CS-SENSE-based MRN to that from SENSE-based MRN plus the 95% confidence intervals (CIs) of these ratios. Results: In the multiple comparison of MRN images with the control of conventional SENSE-based MRN, both the quantitative CR values and the visual score for the CS-SENSE factors of 16 and 32 were significantly lower, whereas the CS-SENSE factors of 4 and 8 showed a non-significant difference. In addition, the quantitative CNR values obtained with the CS-SENSE factors of 4 and 8 were significantly higher than that obtained with the conventional SENSE-based MRN while the CS-SENSE factor of 32 was significantly lower, in contrast, the CS SENSE factors of 16 showed a non-significant difference. For CS-SENSE factors of 4 and 8, all ratios of the CS SENSE-based MRN values for CR, CNR and visual scores to those from SENSE-based MRN were above 0.95. Conclusion: CS-SENSE-based MRN can accomplish fast scanning with sufficient image quality when using a high acceleration factor.

Purpose: To assess the cervical magnetic resonance neurography (MRN) imaging quality obtained with compressed sensing and sensitivity-encoding (compressed SENSE; CS-SENSE) technique in comparison to that obtained with the conventional parallel imaging (i.e., SENSE) technique. Materials and methods: Five healthy volunteers underwent a three-dimensional (3D) turbo spin-echo (TSE)-based cervical MRN examination using a 3.0 Tesla MR-unit. All MRN acquisitions were performed with CS-SENSE and conventional SENSE. We used four acceleration factors (4, 8, 16 and 32) in CS-SENSE. The image quality in MRN was evaluated by assessing the degree of cervical nerve depiction using the contrast ratio (CR) and contrast-noise ratio (CNR) between the cervical nerve and the background signal intensity and a visual scoring system (1: poor, 2: moderate, 3: good). In all of the CR, CNR and visual score, we calculated the ratio of the CS-SENSE-based MRN to that from SENSE-based MRN plus the 95% confidence intervals (CIs) of these ratios. Results: In the multiple comparison of MRN images with the control of conventional SENSE-based MRN, both the quantitative CR values and the visual score for the CS-SENSE factors of 16 and 32 were significantly lower, whereas the CS-SENSE factors of 4 and 8 showed a non-significant difference. In addition, the quantitative CNR values obtained with the CS-SENSE factors of 4 and 8 were significantly higher than that obtained with the conventional SENSE-based MRN while the CS-SENSE factor of 32 was significantly lower, in contrast, the CS SENSE factors of 16 showed a non-significant difference. For CS-SENSE factors of 4 and 8, all ratios of the CS SENSE-based MRN values for CR, CNR and visual scores to those from SENSE-based MRN were above 0.95. Conclusion: CS-SENSE-based MRN can accomplish fast scanning with sufficient image quality when using a high acceleration factor.

Mit ständig wachsenden Datenmengen wird die Aufgabe, zugrunde liegende Struktur zu finden und zu nutzen, immer wichtiger. Eine einflussreiche Erkenntnis, auf die sich moderne Signalverarbeitung wie Compressed Sensing oder Dictionary Learning stützen, ist, dass viele Datentypen eine Art von sparser Darstellung erlauben. Für eine geeignete Basis reicht also eine kleine Anzahl von Elementen aus, um ein beliebiges Signal zu approximieren. Im ersten Teil dieser Arbeit leiten wir technische Ergebnisse her, die es uns ermöglichen, Compressed Sensing und Dictionary Learning in allgemeineren Zusammenhängen zu analysieren, als dies bisher möglich war. Konkret leiten wir Konzentrationsungleichungen für die Operatornorm von zufälligen Submatrizen mit ungleichmäßig verteilten Trägern ab, wobei wir im Wesentlichen zeigen, dass sich die meisten Submatrizen einer gut konditionierten Matrix wie Isometrien verhalten. Bei Compressed Sensing wird ein sparses Signal aus einer möglichst kleinen Anzahl von linearen Messungen rekonstruiert. Wenn diese Messungen aus einer größeren Menge möglicher linearer Messungen durch sampling von einer (möglicherweise ungleichmäßigen) Wahrscheinlichkeitsdichte ausgewählt werden, nennt man dies subsampling (variable density subsampling). Im nächsten Teil der Arbeit leiten wir eine optimale Dichte her, die die Wiederherstellung in einem sehr allgemeinen Setting garantiert. Genauer gesagt zeigen wir, wie die optimale Dichte von der Struktur der Messmatrix und von der Verteilung der sparsen Trägern abhängt, die leicht aus den Daten geschätzt werden können. Dies führt zu einer einfachen Formel für Dichten, die in numerischen Experimenten den neuesten Stand der Technik erreichen. Unser Ansatz lässt sich auch auf strukturierte Erfassungen ausdehnen, bei denen anstelle von Einzelmessungen Blöcke von Messungen vorgenommen werden. In einigen Anwendungen ist die sparsifizierende Basis nicht bekannt oder man möchte eine bessere Basis finden. Das Erlernen einer solc, With ever growing amounts of data, the task of finding and using underlying structure is be- coming more and more important. One influential insight, which modern signal processing tasks like compressed sensing or dictionary learning rely on, is that many data types allow some kind of sparse representation. So given a suitable basis, a small number of elements is sufficient to approximate any given signal. In the first part of this thesis we derive technical results allowing us to analyse compressed sensing and dictionary learning in more general settings than previously possible. Concretely, we derive tail bounds for the operator norm of random submatrices with non-uniformly distributed supports, essentially showing that for a well-conditioned matrix most submatrices behave like an isometry. Compressed sensing consists of reconstructing a sparse signal from a small number of linear measurements. If these measurements are chosen from a bigger set of possible linear measurements via sampling from a (possibly non-uniform) probability distribution, this is called (variable density) subsampling. In the next part of the thesis we derive an optimal subsampling density, guaranteeing recovery in a very general setting. More precisely, we show how the optimal subsampling density depends on the structure of the sensing matrix and on the distribution of the sparse supports, which can easily be estimated from data. This leads to a simple formula for subsampling densities achieving state of the art performance in numerical experiments. Our approach also extends to structured acquisition, where instead of isolated measurements, blocks of measurements are taken. In some applications the sparsifying basis is not known or one wants to find a better one. Learning such a basis from data is called dictionary learning. In the third part of this thesis we study the convergence behaviour of two of the most popular dictionary learning algorithms - the Method of Optimal Directions (MOD) and, submitted by Simon Ruetz, Kumulative Dissertation aus zwei Artikeln, Dissertation University of Innsbruck 2022

Recent years have witnessed an increasing popularity of wireless body area network (WBAN), with which continuous collection of physiological signals can be conveniently performed for healthcare monitoring. Energy consumption is a critical issue because it directly affects the duration of the equipped sensors. In this paper, we propose a low-cost and confidential electrocardiogram (ECG) acquisition approach for WBAN. The compressed sensing (CS) is employed for low-cost signal acquisition, and its cryptographic features are exploited for promoting the framework's confidentiality. In particular, the RIPless measurement matrix is used to give CS the resistance against plaintext attack, while the first-order $\Sigma \Delta$ quantizer is employed to embed the cryptographic diffusion feature into the whole system. Two chaotic systems are employed for generating the required secret elements for the acquisition and encryption. Experiment results well demonstrate the signal reconstruction and security performance of the proposed framework., Export Date: 29 December 2022; Article; CODEN: ITIBF

This work considers a collocated radar scenario where a probing signal is emitted toward the targets of interest and records the received echoes. Estimating the relative delay-Doppler shifts of the targets allows determining their relative locations and velocities. However, the received radar measurements are often affected by impulsive non-Gaussian noise which makes a few measurements partially corrupted. While demixing radar signal and impulsive noise is challenging in general by traditional subspace-based methods, atomic norm minimization (ANM) has been recently developed to perform this task in a much more efficient manner. Nonetheless, the ANM cannot identify close delay-Doppler pairs and also requires many measurements. Here, we propose a smoothed l(0) atomic optimization problem encouraging both the sparse features of the targets and the impulsive noise. We design a majorization-minimization algorithm that converges to the solution of the proposed non-convex problem using alternating direction method of multipliers (ADMM). Simulations results verify the superior accuracy of our proposed algorithm even for very close delay-Doppler pairs in comparison to ANM with around 40 dB improvement., QC 20221202

Fitness functions map biological sequences to a scalar property of interest. Accurate estimation of these functions yields biological insight and sets the foundation for model-based sequence design. However, the fitness datasets available to learn these functions are typically small relative to the large combinatorial space of sequences; characterizing how much data are needed for accurate estimation remains an open problem. There is a growing body of evidence demonstrating that empirical fitness functions display substantial sparsity when represented in terms of epistatic interactions. Moreover, the theory of Compressed Sensing provides scaling laws for the number of samples required to exactly recover a sparse function. Motivated by these results, we develop a framework to study the sparsity of fitness functions sampled from a generalization of the NK model, a widely used random field model of fitness functions. In particular, we present results that allow us to test the effect of the Generalized NK (GNK) model's interpretable parameters-sequence length, alphabet size, and assumed interactions between sequence positions-on the sparsity of fitness functions sampled from the model and, consequently, the number of measurements required to exactly recover these functions. We validate our framework by demonstrating that GNK models with parameters set according to structural considerations can be used to accurately approximate the number of samples required to recover two empirical protein fitness functions and an RNA fitness function. In addition, we show that these GNK models identify important higher-order epistatic interactions in the empirical fitness functions using only structural information.

ObjectivesThis study aimed at developing dictionary learning (DL) based compressed sensing (CS) reconstruction for randomly undersampled five-dimensional (5D) MR Spectroscopic Imaging (3D spatial + 2D spectral) data acquired in prostate cancer patients and healthy controls, and test its feasibility at 8x and 12x undersampling factors.Materials and methodsProspectively undersampled 5D echo-planar J-resolved spectroscopic imaging (EP-JRESI) data were acquired in nine prostate cancer (PCa) patients and three healthy males. The 5D EP-JRESI data were reconstructed using DL and compared with gradient sparsity-based Total Variation (TV) and Perona-Malik (PM) methods. A hybrid reconstruction technique, Dictionary Learning-Total Variation (DLTV), was also designed to further improve the quality of reconstructed spectra.ResultsThe CS reconstruction of prospectively undersampled (8x and 12x) 5D EP-JRESI data acquired in prostate cancer and healthy subjects were performed using DL, DLTV, TV and PM. It is evident that the hybrid DLTV method can unambiguously resolve 2D J-resolved peaks including myo-inositol, citrate, creatine, spermine and choline.ConclusionImproved reconstruction of the accelerated 5D EP-JRESI data was observed using the hybrid DLTV. Accelerated acquisition of in vivo 5D data with as low as 8.33% samples (12x) corresponds to a total scan time of 14 min as opposed to a fully sampled scan that needs a total duration of 2.4 h (TR = 1.2 s, 32 [Formula: see text]×16 [Formula: see text]×8 [Formula: see text], 512 [Formula: see text] and 64 [Formula: see text]).

We present a retrospective joint motion correction and reconstruction scheme for magnetic resonance imaging to reduce the imprint of subject motion on the reconstructed images. In multi-contrast imaging, reconstructions pertaining to distinct acquisition sequences (e.g., T1 or T2 weighted images) might not be equally affected by motion, due to the sequential nature of the data acquisition process or the specific sequence design. To avoid repeating the corrupted scan, we can leverage the uncorrupted reconstructions to post-process the contrasts that are most severely affected by motion, by assuming a shared underlying anatomy. Only rigid motion is considered here, but no further assumptions are required. Classical motion correction schemes are combined with weighted total-variation regularization, whose weight is defined by the structure of the well-resolved contrasts. We will particularly focus on brain imaging with conventional Cartesian sampling. We envision a practical workflow that can easily fit into the existing clinical practice without the need for changing the MRI acquisition protocols.

A main goal of data-driven materials research is to find optimal low-dimensional descriptors, allowing us to predict a physical property, and to interpret them in a human-understandable way. In this work, we advance methods to identify descriptors out of a large pool of candidate features by means of compressed sensing. To this extent, we develop schemes for engineering appropriate candidate features that are based on simple basic properties of building blocks that constitute the materials and that are able to represent a multi-component system by scalar numbers. Cross-validation based feature-selection methods are developed for identifying the most relevant features, thereby focusing on high generalizability. We apply our approaches to an ab initio dataset of ternary group-IV compounds to obtain a set of descriptors for predicting lattice constants and energies of mixing. In particular, we introduce simple complexity measures in terms of involved algebraic operations as well as the amount of utilized basic properties., Horizon 2020 Framework Programmehttp://dx.doi.org/10.13039/100010661, Peer Reviewed