Search

Current spatiotemporal deep learning approaches to Magnetic Resonance Fingerprinting (MRF) build artefact-removal models customised to a particular k-space subsampling pattern which is used for fast (compressed) acquisition. This may not be useful when the acquisition process is unknown during training of the deep learning model and/or changes during testing time. This paper proposes an iterative deep learning plug-and-play reconstruction approach to MRF which is adaptive to the forward acquisition process. Spatiotemporal image priors are learned by an image denoiser i.e. a Convolutional Neural Network (CNN), trained to remove generic white gaussian noise (not a particular subsampling artefact) from data. This CNN denoiser is then used as a data-driven shrinkage operator within the iterative reconstruction algorithm. This algorithm with the same denoiser model is then tested on two simulated acquisition processes with distinct subsampling patterns. The results show consistent dealiasing performance against both acquisition schemes and accurate mapping of tissues' quantitative bio-properties. Software available: https://github.com/ketanfatania/QMRI-PnP-Recon-POC

Purpose Advanced MRI-based biomarkers offer comprehensive and quantitative information for the evaluation and characterization of brain tumors. In this study, we report initial clinical experience in routine glioma imaging with a novel, fully 3D multiparametric quantitative transient-state imaging (QTI) method for tissue characterization based on T1 and T2 values. Methods To demonstrate the viability of the proposed 3D QTI technique, nine glioma patients (grade II–IV), with a variety of disease states and treatment histories, were included in this study. First, we investigated the feasibility of 3D QTI (6:25 min scan time) for its use in clinical routine imaging, focusing on image reconstruction, parameter estimation, and contrast-weighted image synthesis. Second, for an initial assessment of 3D QTI-based quantitative MR biomarkers, we performed a ROI-based analysis to characterize T1 and T2 components in tumor and peritumoral tissue. Results The 3D acquisition combined with a compressed sensing reconstruction and neural network-based parameter inference produced parametric maps with high isotropic resolution (1.125 × 1.125 × 1.125 mm3 voxel size) and whole-brain coverage (22.5 × 22.5 × 22.5 cm3 FOV), enabling the synthesis of clinically relevant T1-weighted, T2-weighted, and FLAIR contrasts without any extra scan time. Our study revealed increased T1 and T2 values in tumor and peritumoral regions compared to contralateral white matter, good agreement with healthy volunteer data, and high inter-subject consistency. Conclusion 3D QTI demonstrated comprehensive tissue assessment of tumor substructures captured in T1 and T2 parameters. Aiming for fast acquisition of quantitative MR biomarkers, 3D QTI has potential to improve disease characterization in brain tumor patients under tight clinical time-constraints.

Novel methods for quantitative, transient-state multiparametric imaging are increasingly being demonstrated for assessment of disease and treatment efficacy. Here, we build on these by assessing the most common Non-Cartesian readout trajectories (2D/3D radials and spirals), demonstrating efficient anti-aliasing with a k-space view-sharing technique, and proposing novel methods for parameter inference with neural networks that incorporate the estimation of proton density. Our results show good agreement with gold standard and phantom references for all readout trajectories at 1.5T and 3T. Parameters inferred with the neural network were within 6.58% difference from the parameters inferred with a high-resolution dictionary. Concordance correlation coefficients were above 0.92 and the normalized root mean squared error ranged between 4.2% - 12.7% with respect to gold-standard phantom references for T1 and T2. In vivo acquisitions demonstrate sub-millimetric isotropic resolution in under five minutes with reconstruction and inference times < 7 minutes. Our 3D quantitative transient-state imaging approach could enable high-resolution multiparametric tissue quantification within clinically acceptable acquisition and reconstruction times., 43 pages, 12 Figures, 5 Tables

We propose a novel numerical approach to separate multiple tissue compartments in image voxels and to estimate quantitatively their nuclear magnetic resonance (NMR) properties and mixture fractions, given magnetic resonance fingerprinting (MRF) measurements. The number of tissues, their types or quantitative properties are not a-priori known, but the image is assumed to be composed of sparse compartments with linearly mixed Bloch magnetisation responses within voxels. Fine-grid discretisation of the multi-dimensional NMR properties creates large and highly coherent MRF dictionaries that can challenge scalability and precision of the numerical methods for (discrete) sparse approximation. To overcome these issues, we propose an off-the-grid approach equipped with an extended notion of the sparse group Lasso regularisation for sparse approximation using continuous (non-discretised) Bloch response models. Furthermore, the nonlinear and non-analytical Bloch responses are approximated by a neural network, enabling efficient back-propagation of the gradients through the proposed algorithm. Through numerical experiments on simulated and in vivo healthy brain MRF data, we demonstrate the effectiveness of the proposed scheme compared to baseline multi-compartment MRF methods.

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature to have optimal complexities in theory, and provide great improvement empirically over the deterministic gradient methods. Surprisingly, in some tasks such as image deblurring, many of such methods fail to converge faster than the accelerated deterministic gradient methods, even in terms of epoch counts. We investigate this phenomenon and propose a theory-inspired mechanism for the practitioners to efficiently characterize whether it is beneficial for an inverse problem to be solved by stochastic optimization techniques or not. Using standard tools in numerical linear algebra, we derive conditions on the spectral structure of the inverse problem for being a suitable application of stochastic gradient methods. Particularly, we show that, for an imaging inverse problem, if and only if its Hessain matrix has a fast-decaying eigenspectrum, then the stochastic gradient methods can be more advantageous than deterministic methods for solving such a problem. Our results also provide guidance on choosing appropriately the partition minibatch schemes, showing that a good minibatch scheme typically has relatively low correlation within each of the minibatches. Finally, we propose an accelerated primal-dual SGD algorithm in order to tackle another key bottleneck of stochastic optimization which is the heavy computation of proximal operators. The proposed method has fast convergence rate in practice, and is able to efficiently handle non-smooth regularization terms which are coupled with linear operators.

Consistency of the predictions with respect to the physical forward model is pivotal for reliably solving inverse problems. This consistency is mostly un-controlled in the current end-to-end deep learning methodologies proposed for the Magnetic Resonance Fingerprinting (MRF) problem. To address this, we propose PGD-Net, a learned proximal gradient descent framework that directly incorporates the forward acquisition and Bloch dynamic models within a recurrent learning mechanism. The PGD-Net adopts a compact neural proximal model for de-aliasing and quantitative inference, that can be flexibly trained on scarce MRF training datasets. Our numerical experiments show that the PGD-Net can achieve a superior quantitative inference accuracy, much smaller storage requirement, and a comparable runtime to the recent deep learning MRF baselines, while being much faster than the dictionary matching schemes. Code has been released at https://github.com/edongdongchen/PGD-Net.

Purpose High-resolution isotropic T-2 mapping of the human brain with multi-echo spin-echo (MESE) acquisitions is challenging. When using a 2D sequence, the resolution is limited by the slice thickness. If used as a 3D acquisition, specific absorption rate limits are easily exceeded due to the high power deposition of nonselective refocusing pulses. A method to reconstruct 1-mm(3) isotropic T-2 maps is proposed based on multiple 2D MESE acquisitions. Data were undersampled (10-fold) to compensate for the prolonged scan time stemming from the super-resolution acquisition. Theory and Methods The proposed method integrates a classical super-resolution with an iterative model-based approach to reconstruct quantitative maps from a set of undersampled low-resolution data. The method was tested on numerical and multipurpose phantoms, and in vivo data. T-2 values were assessed with a region-of-interest analysis using a single-slice spin-echo and a fully sampled MESE acquisition in a phantom, and a MESE acquisition in healthy volunteers. Results Numerical simulations showed that the best trade-off between acceleration and number of low-resolution datasets is 10-fold acceleration with 4 acquisitions (acquisition time = 18 min). The proposed approach showed improved resolution over low-resolution images for both phantom and brain. Region-of-interest analysis of the phantom compartments revealed that at shorter T-2, the proposed method was comparable with the fully sampled MESE. For the volunteer data, the T-2 values found in the brain structures were consistent across subjects (8.5-13.1 ms standard deviation). Conclusion The proposed method addresses the inherent limitations associated with high-resolution T-2 mapping and enables the reconstruction of 1 mm(3) isotropic relaxation maps with a 10 times faster acquisition.

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study a deep learning approach to address these shortcomings. Coupled with a dimensionality reduction first layer, the proposed MRF-Net is able to reconstruct quantitative maps by saving more than 60 times in memory and computations required for a DM baseline. Fine-grid manifold enumeration i.e. the MRF dictionary is only used for training the network and not during image reconstruction. We show that the MRF-Net provides a piece-wise affine approximation to the Bloch response manifold projection and that rather than memorizing the dictionary, the network efficiently clusters this manifold and learns a set of hierarchical matched-filters for affine regression of the NMR characteristics in each segment.

Purpose: To develop an accelerated Cartesian MRF implementation using a multi-shot EPI sequence for rapid simultaneous quantification of T1 and T2 parameters. Methods: The proposed Cartesian MRF method involved the acquisition of highly subsampled MR images using a 16-shot EPI readout. A linearly varying flip angle train was used for rapid, simultaneous T1 and T2 quantification. The accuracy of parametric map estimations were improved by using an iterative projection algorithm. The results were compared to a conventional spiral MRF implementation. The acquisition time per slice was 8s and this method was validated on a phantom and a healthy volunteer brain in vivo. Results: Joint T1 and T2 estimations using the 16-shot EPI readout are in good agreement with the spiral implementation using the same acquisition parameters (deviation less than 3% for T1 and less than 4% for T2) for the healthy volunteer brain. The T1 and T2 values also agree with the conventional values previously reported in the literature. The visual quality of the multi-parametric maps generated by the multi-shot EPI-MRF and spiral-MRF implementations were comparable. Conclusion: The multi-shot EPI-MRF method generated accurate quantitative multi-parametric maps similar to conventional Spiral - MRF. This multi-shot approach achieved provides an alternative for performing MRF using an accelerated Cartesian readout, thereby increasing the potential usability of MRF., Comment: 12 pages, 11 main figures, 2 supplementry figures, preprint of accepted abstract

We propose a dictionary-matching-free pipeline for multi-parametric quantitative MRI image computing. Our approach has two stages based on compressed sensing reconstruction and deep learned quantitative inference. The reconstruction phase is convex and incorporates efficient spatiotemporal regularisations within an accelerated iterative shrinkage algorithm. This minimises the under-sampling (aliasing) artefacts from aggressively short scan times. The learned quantitative inference phase is purely trained on physical simulations (Bloch equations) that are flexible for producing rich training samples. We propose a deep and compact encoder-decoder network with residual blocks in order to embed Bloch manifold projections through multi-scale piecewise affine approximations, and to replace the non-scalable dictionary-matching baseline. Tested on a number of datasets we demonstrate effectiveness of the proposed scheme for recovering accurate and consistent quantitative information from novel and aggressively subsampled 2D/3D quantitative MRI acquisition protocols.

We study the convergence of the iterative projected gradient (IPG) algorithm for arbitrary (possibly non-convex) sets when both the gradient and projection oracles are computed approximately. We consider different notions of approximation of which we show that the progressive fixed precision and the $(1+ \varepsilon)$ -optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We show that the former scheme is also able to maintain the (linear) rate of convergence of the exact algorithm under the same embedding assumption. In contrast, the $(1+ \varepsilon)$ -approximate oracle requires a stronger embedding condition, moderate compression ratios and it typically slows down the convergence. We apply our results to accelerate solving a class of data driven compressed sensing problems, where we replace iterative exhaustive searches over large data sets by fast approximate nearest neighbor search strategies based on the cover tree data structure. For data sets with low intrinsic dimensions, our proposed algorithm achieves a complexity logarithmic in terms of the data set population as opposed to the linear complexity of a brute force search. By running several numerical experiments, we conclude similar observations as predicted by our theoretical analysis.

Sensor selection refers to the problem of intelligently selecting a small subset of a collection of available sensors to reduce the sensing cost while preserving signal acquisition performance. The majority of sensor selection algorithms find the subset of sensors that best recovers an arbitrary signal from a number of linear measurements that is larger than the dimension of the signal. In this paper, we develop a new sensor selection algorithm for sparse (or near sparse) signals that finds a subset of sensors that best recovers such signals from a number of measurements that is much smaller than the dimension of the signal. Existing sensor selection algorithms cannot be applied in such situations. Our proposed Incoherent Sensor Selection (Insense) algorithm minimizes a coherence-based cost function that is adapted from recent results in sparse recovery theory. Using six datasets, including two real-world datasets on microbial diagnostics and structural health monitoring, we demonstrate the superior performance of Insense for sparse-signal sensor selection.

Sketched gradient algorithms have been recently introduced for efficiently solving the large-scale constrained Least-squares regressions. In this paper we provide novel convergence analysis for the basic method {\it Gradient Projection Classical Sketch} (GPCS) to reveal the fast linear convergence rate of GPCS towards a vicinity of the solution thanks to the intrinsic low-dimensional geometric structure of the solution prompted by constraint set. Similar to our analysis we observe computational and sketch size trade-offs in numerical experiments. Hence we justify that the combination of gradient methods and the sketching technique is a way of designing efficient algorithms which can actively exploit the low-dimensional structure to accelerate computation in large scale data regression and signal processing applications., 7 pages

We adopt a data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Leveraging on the recent stability results for the inexact Iterative Projected Gradient (IPG) algorithm and by using the cover tree's ANN searches, we decrease the projection cost of the IPG algorithm to be logarithmically growing with data population for low dimensional smooth manifolds. We apply our results to quantitative MRI compressed sensing and in particular within the Magnetic Resonance Fingerprinting (MRF) framework. For a similar (or sometimes better) reconstruction accuracy, we report 2–3 orders of magnitude reduction in computations compared to the standard iterative method, which uses brute-force searches.

Current popular methods for magnetic resonance fingerprint (MRF) recovery are bottlenecked by the heavy computations of a matched-filtering step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. We address this shortcoming by arranging dictionary atoms in the form of cover tree structures and adopt the corresponding fast approximate nearest neighbour searches to accelerate matched-filtering. For datasets belonging to smooth low-dimensional manifolds cover trees offer search complexities logarithmic in terms of data population. With this motivation we propose an iterative reconstruction algorithm, named CoverBLIP, to address large-size MRF problems where the fingerprint dictionary i.e. discrete manifold of Bloch responses, encodes several intrinsic NMR parameters. We study different forms of convergence for this algorithm and we show that provided with a notion of embedding, the inexact and non-convex iterations of CoverBLIP linearly convergence toward a near-global solution with the same order of accuracy as using exact brute-force searches. Our further examinations on both synthetic and real-world datasets and using different sampling strategies, indicates between 2–3 orders of magnitude reduction in total search computations. Cover trees are robust against the curse-of-dimensionality and therefore CoverBLIP provides a notion of scalability—a consistent gain in time-accuracy performance—for searching high-dimensional atoms which may not be easily preprocessed (i.e. for dimensionality reduction) due to the increasing degrees of non-linearities appearing in the emerging multi-parametric MRF dictionaries.

With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS) techniques, which exploit the sparsity of signals, have allowed to reconstruct signal and images with less measurements than the traditional Nyquist sensing approach. However, multichannel signals like Hyperspectral images (HSI) have additional structures, like inter-channel correlations, that are not taken into account in the classical CS scheme. In this paper we exploit the linear mixture of sources model, that is the assumption that the multichannel signal is composed of a linear combination of sources, each of them having its own spectral signature, and propose new sampling schemes exploiting this model to considerably decrease the number of measurements needed for the acquisition and source separation. Moreover, we give theoretical lower bounds on the number of measurements required to perform reconstruction of both the multichannel signal and its sources. We also proposed optimization algorithms and extensive experimentation on our target application which is HSI, and show that our approach recovers HSI with far less measurements and computational effort than traditional CS approaches., 32 pages

This article does not present new mathematical results, it solely aims at discussing some numerical experiments with MALDI Imaging data. However, these experiments are based on and could not be done without the mathematical results obtained in the UNLocX project. They tackle two obstacles which presently prevent clinical routine applications of MALDI Imaging technology. In the last decade, matrix-assisted laser desorption/ionization imaging mass spectrometry (MALDI-IMS) has developed into a powerful bioanalytical imaging modality. MALDI imaging data consists of a set of mass spectra, which are measured at different locations of a flat tissue sample. Hence, this technology is capable of revealing the full metabolic structure of the sample under investigation. Sampling resolution as well as spectral resolution is constantly increasing, presently a conventional 2D MALDI Imaging data requires up to 100 GB per dataset. A major challenge towards routine applications of MALDI Imaging in pharmaceutical or medical workflows is the high computational cost for evaluating and visualizing the information content of MALDI imaging data. This becomes even more critical in the near future when considering cohorts or 3D applications. Due to its size and complexity MALDI Imaging constitutes a challenging test case for high performance signal processing. In this article we will apply concepts and algorithms, which were developed within the UNLocX project, to MALDI Imaging data. In particular we will discuss a suitable phase space model for such data and report on implementations of the resulting transform coders using GPU technology. Within the MALDI Imaging workflow this leads to an efficient baseline removal and peak picking. The final goal of data processing in MALDI Imaging is the discrimination of regions having different metabolic structures. We introduce and discuss so-called soft-segmentation maps which are obtained by non-negative matrix factorization incorporating sparsity constraints.

Detecting and tracking people in scenes monitored by cameras is an important step in many application scenarios such as surveillance, urban planning or behavioral studies to name a few. The amount of data produced by camera feeds is so large that it is also vital that these steps be performed with the utmost computational efficiency and often even real-time. We propose SCOOP, a novel algorithm that reliably detects pedestrians in camera feeds, using only the output of a simple background removal technique. SCOOP can handle a single or many video feeds. At the heart of our technique there is a sparse model for binary motion detection maps that we solve with a novel greedy algorithm based on set covering. We study the convergence and performance of the algorithm under various degradation models such as noisy observations and crowded environments, and we provide mathematical and experimental evidence of both its efficiency and robustness using standard datasets. This clearly shows that SCOOP is a viable alternative to existing state-of-the-art people detection algorithms, with the marked advantage of real-time computations.

International audience; Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied regularization models with various types of low-dimensional structures. In such settings, the general approach is to solve a regularized optimization problem, which combines a data fidelity term and some regularization penalty that promotes the assumed low-dimensional/simple structure. This paper provides a general framework to capture this low-dimensional structure through what we coin partly smooth functions relative to a linear manifold. These are convex, non-negative, closed and finite-valued functions that will promote objects living on low-dimensional subspaces. This class of regularizers encompasses many popular examples such as the L1 norm, L1-L2 norm (group sparsity), as well as several others including the Linfty norm. We also show that the set of partly smooth functions relative to a linear manifold is closed under addition and pre-composition by a linear operator, which allows to cover mixed regularization, and the so-called analysis-type priors (e.g. total variation, fused Lasso, finite-valued polyhedral gauges). Our main result presents a unified sharp analysis of exact and robust recovery of the low-dimensional subspace model associated to the object to recover from partial measurements. This analysis is illustrated on a number of special and previously studied cases, and on an analysis of the performance of Linfty regularization in a compressed sensing scenario.

We tackle the speech separation problem through modeling the acoustics of the reverberant chambers. Our approach exploits structured sparsity models to perform speech recovery and room acoustic modeling from recordings of concurrent unknown sources. The speakers are assumed to lie on a two-dimensional plane and the multipath channel is characterized using the image model. We propose an algorithm for room geometry estimation relying on localization of the early images of the speakers by sparse approximation of the spatial spectrum of the virtual sources in a free-space model. The images are then clustered exploiting the low-rank structure of the spectro-temporal components belonging to each source. This enables us to identify the early support of the room impulse response function and its unique map to the room geometry. To further tackle the ambiguity of the reflection ratios, we propose a novel formulation of the reverberation model and estimate the absorption coefficients through a convex optimization exploiting joint sparsity model formulated upon spatio-spectral sparsity of concurrent speech representation. The acoustic parameters are then incorporated for separating individual speech signals through either structured sparse recovery or inverse filtering the acoustic channels. The experiments conducted on real data recordings of spatially stationary sources demonstrate the effectiveness of the proposed approach for speech separation and recognition.

This paper presents a novel approach to capture light field in camera arrays based on the compressive sensing framework. Light fields are captured by a linear array of cameras with overlapping field of view. In this work, we design a redundant dictionary to exploit cross-cameras correlated structures to sparsely represent cameras image. Our main contributions are threefold. First, we exploit the correlations between the set of views by making use of a specially designed redundant dictionary. We show experimentally that the projection of complex scenes onto this dictionary yields very sparse coefficients. Second, we propose an efficient compressive encoding scheme based on the random convolution framework [1]. Finally, we develop a joint sparse recovery algorithm for decoding the compressed measurements and show a marked improvement over independent decoding of CS measurements.

In this paper we propose a novel and efficient model for compressed sensing of hyperspectral images. A large-size hyperspectral image can be subsampled by retaining only 3\% of its original size, yet robustly recovered using the new approach we present here. Our reconstruction approach is based on minimizing a convex functional which penalizes both the trace norm and the TV norm of the data matrix. Thus, the solution tends to have a simultaneous low-rank and piecewise smooth structure: the two important priors explaining the underlying correlation structure of such data. Through simulations we will show our approach significantly enhances the conventional compression rate-distortion tradeoffs. In particular, in the strong undersampling regimes our method outperforms the standard TV denoising image recovery scheme by more than 17dB in the reconstruction MSE.

This paper analyzes the performance of the simple thresholding algorithm for sparse signal representations. In particular, in order to be more realistic we introduce a new probabilistic signal model which assumes randomness for both the amplitude and also the location of nonzero entries. Based on this model we show that thresholding in average can correctly recover signals for much higher sparsity levels than was previously reported. The bounds we obtain in this paper are based on a new concept of average dictionary coherence and are shown to be much sharper than in former works [1,2].

We propose a novel approach to reconstruct Hyperspectral images from very few number of noisy compressive measure- ments. Our reconstruction approach is based on a convex minimiza- tion which penalizes both the nuclear norm and the l2,1 mixed-norm of the data matrix. Thus, the solution tends to have a simultane- ously low-rank and joint-sparse structure. We explain how these two assumptions fit the Hyperspectral data, and by severals simulations we show that our proposed reconstruction scheme significantly enhances the state-of-the-art tradeoffs between the reconstruction error and the required number of CS measurements.

This paper describes a novel framework for compressive sampling (CS) of multichannel signals that are highly dependent across the channels. In this work, we assume few number of sources are generating the multichannel observations based on a linear mixture model. Moreover, sources are assumed to have sparse/compressible representations in some orthonormal basis. The main contribution of this paper lies in 1) rephrasing the CS acquisition of multichannel data as a compressive blind source separation problem, and 2) proposing an optimization problem and a recovery algorithm to estimate both the sources and the mixing matrix (and thus the whole data) from the compressed measurements. A number of experiments on the acquisition of Hyperspectral images show that our proposed algorithm obtains a reconstruction error between 10 dB and 15 dB less than other state-of-the-art CS methods.

Distributed compressed sensing is the extension of compressed sampling (CS) to sensor networks. The idea is to design a CS joint decoding scheme at a central decoder (base station) that exploits the inter-sensor correlations, in order to recover the whole observations from very few number of random measurements per node. In this paper, we focus on modeling the correlations and on the design and analysis of efficient joint recovery algorithms. We show, by extending earlier results of Baron et al.,1 that a simple thresholding algorithm can exploit the full diversity offered by all channels to identify a common sparse support using a near optimal number of measurements.