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Sparse regression is employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data is the presence of correlations between predictive features. These correlations hamper both feature selection and estimation and jeopardize conclusions drawn from estimated models. On the other hand, theoretical results on sparsity-inducing regularized regression have largely addressed conditions for selection consistency via asymptotics, and disregard the problem of model selection, whereby regularization parameters are chosen. In this numerical study, we address these issues through exhaustive characterization of the performance of several regression estimators, coupled with a range of model selection strategies. These estimators and selection criteria were examined across correlated regression problems with varying degrees of signal to noise, distributions of non-zero model coefficients, and model sparsity. Our results reveal a fundamental tradeoff between false positive and false negative control in all regression estimators and model selection criteria examined. Additionally, we numerically explore a transition point modulated by the signal-to-noise ratio and spectral properties of the design covariance matrix at which the selection accuracy of all considered algorithms degrades. Overall, we find that SCAD coupled with BIC or empirical Bayes model selection performs the best feature selection across the regression problems considered. [ABSTRACT FROM AUTHOR]

Beamspace processing is widely applied in Direction‐of‐Arrival (DOA) estimation thanks to dimensional reduction and super‐resolution characterisations. However, the conventional atomic norm minimisation (ANM) based methods for beamspace DOA estimation are of high computational complexity for large arrays. To deal with this issue, the proposed method focuses on locating the sources in the mainlobe of the beamspace and encodes such prior information into the ANM problem without frequency‐selective constraints. The proposed method approximates the beamspace array manifold in the mainlobe sector with the truncated sector Fourier series. The theoretical analysis shows that such approximation with the properly designed fitting error relaxation on the boundary yields the low dimensional semidefinite programming (SDP) approximate implementation of the proposed ANM method and guarantees the support recovery inside the mainlobe. Furthermore, the low complexity Burer‐Monteiro factorisation based alternating direction method of multipliers method is proposed to solve the SDP problem. The complexity analysis and simulations show that the proposed method results in significant computational complexity reduction and slightly better performance compared with state‐of‐art benchmarks. [ABSTRACT FROM AUTHOR]

When traditional EEG signals are collected based on the Nyquist theorem, long-time recordings of EEG signals will produce a large amount of data. At the same time, limited bandwidth, end-to-end delay, and memory space will bring great pressure on the effective transmission of data. The birth of compressed sensing alleviates this transmission pressure. However, using an iterative compressed sensing reconstruction algorithm for EEG signal reconstruction faces complex calculation problems and slow data processing speed, limiting the application of compressed sensing in EEG signal rapid monitoring systems. As such, this paper presents a non-iterative and fast algorithm for reconstructing EEG signals using compressed sensing and deep learning techniques. This algorithm uses the improved residual network model, extracts the feature information of the EEG signal by one-dimensional dilated convolution, directly learns the nonlinear mapping relationship between the measured value and the original signal, and can quickly and accurately reconstruct the EEG signal. The method proposed in this paper has been verified by simulation on the open BCI contest dataset. Overall, it is proved that the proposed method has higher reconstruction accuracy and faster reconstruction speed than the traditional CS reconstruction algorithm and the existing deep learning reconstruction algorithm. In addition, it can realize the rapid reconstruction of EEG signals. [ABSTRACT FROM AUTHOR]

This paper introduces a golden ratio proximal gradient alternating direction method of multipliers (GRPG-ADMM) for distributed composite convex optimization. When applied to the consensus optimization problem, the GRPG-ADMM provides a superior safety protection approach to computing an optimal decision for a network of agents connected by edges in an undirected graph. To ensure convergence, we expand the parameter range used in the convex combination step. The algorithm has been implemented to solve a decentralized composite convex consensus optimization problem, resulting in a single-loop decentralized golden ratio proximal gradient algorithm. Notably, the agents do not need to communicate with their neighbors before launching the algorithm. Our algorithm guarantees convergence for both primal and dual iterates, with an ergodic convergence rate of O (1 / k) measured by function value residual and consensus violation. To demonstrate the efficiency of the algorithm, we compare its performance with two state-of-the-art algorithms and present numerical results on the decentralized sparse group LASSO problem and the decentralized compressed sensing problem. [ABSTRACT FROM AUTHOR]

Reconstruction of discretely sampled geophysical data is generally done via gridding or interpolant algorithms. Such approaches typically consider local gradients which, while emphasising small-scale structure, can also introduce gridding artefacts, and modify the frequency characteristics of the original data. Here, we examine the potential of compressed sensing techniques for spatially-varying geophysical data, particularly line and gridded aeromagnetic data. We show that for sub-Nyquist sampling rates, the approach is still able to reconstruct a legible signal, and demonstrate the frequency representation of the reconstructed data varies with data sampling frequency, showing a reduced frequency range for sparser sampling. In contrast, we demonstrate that many widespread gridding approaches artificially introduce high-frequency signals into the gridded maps that are not present in the original nor in the compressed sensing reconstructions. This demonstrates the limitations of conventional gridding approaches in spectral fidelity and also suggests the conditions under which compressed sensing may be a more appropriate interpolant technique – namely when authentic spectral representation of the data is of higher precedent than small-scale target identification. [ABSTRACT FROM AUTHOR]

A computational spectrometer is a novel form of spectrometer powerful for portable in situ applications. In the encoding part of the computational spectrometer, filters with highly non-correlated properties are requisite for compressed sensing, which poses severe challenges for optical design and fabrication. In the reconstruction part of the computational spectrometer, conventional iterative reconstruction algorithms are featured with limited efficiency and accuracy, which hinders their application for real-time in situ measurements. This study proposes a neural network computational spectrometer trained by a small dataset with high-correlation optical filters. We aim to change the paradigm by which the accuracy of neural network computational spectrometers depends heavily on the amount of training data and the non-correlation property of optical filters. First, we propose a presumption about a distribution law for the common large training dataset, in which a unique widespread distribution law is shown when calculating the spectrum correlation. Based on that, we extract the original dataset according to the distribution probability and form a small training dataset. Then a fully connected neural network architecture is constructed to perform the reconstruction. After that, a group of thin film filters are introduced to work as the encoding layer. Then the neural network is trained by a small dataset under high-correlation filters and applied in simulation. Finally, the experiment is carried out and the result indicates that the neural network enabled by a small training dataset has performed very well with the thin film filters. This study may provide a reference for computational spectrometers based on high-correlation optical filters. [ABSTRACT FROM AUTHOR]

Background: Deep learning methods driven by the low‐rank regularization have achieved attractive performance in dynamic magnetic resonance (MR) imaging. The effectiveness of existing methods lies mainly in their ability to capture interframe relationships using network modules, which are lack interpretability. Purpose: This study aims to design an interpretable methodology for modeling interframe relationships using convolutiona networks, namely Annihilation‐Net and use it for accelerating dynamic MRI. Methods: Based on the equivalence between Hankel matrix product and convolution, we utilize convolutional networks to learn the null space transform for characterizing low‐rankness. We employ low‐rankness to represent interframe correlations in dynamic MR imaging, while combining with sparse constraints in the compressed sensing framework. The corresponding optimization problem is solved in an iterative form with the semi‐quadratic splitting method (HQS). The iterative steps are unrolled into a network, dubbed Annihilation‐Net. All the regularization parameters and null space transforms are set as learnable in the Annihilation‐Net. Results: Experiments on the cardiac cine dataset show that the proposed model outperforms other competing methods both quantitatively and qualitatively. The training set and test set have 800 and 118 images, respectively. Conclusions: The proposed Annihilation‐Net improves the reconstruction quality of accelerated dynamic MRI with better interpretability. [ABSTRACT FROM AUTHOR]

Structural modal estimation has consistently remained one of the most crucial areas of research in mechanical vibration analysis and signal processing. It is imperative to accurately monitor the vibration signals of rotor blades and their corresponding structural modal parameters. Blade tip timing (BTT) is a promising approach used to measure vibration and monitor the health of blades. However, most existing BTT methods focus on frequency accuracy, neglecting damping, a key physical quantity that represents the strength of the structure. This research focuses on damping modal estimation of blade vibration and proposes a sparse reconstruction algorithm based on a two-dimensional Laplace wavelet family, which addresses the inherent under-sampled problem of BTT technology while enabling estimations of both the structural modal frequency and modal damping of the blades. Firstly, the proposed algorithm is achieved by designing a Laplace wavelet dictionary based on prior information and using a convex optimization objective function with a regularization term. Secondly, Laplace wavelet dictionary matches the signal better than the traditional Fourier dictionary based on the similarity between the damped vibration signal and the Laplace wavelet, then a sparser representation vector can be obtained. Moreover, the research object is not limited to a single blade, but can be easily expanded to multiple stages and multiple rotating blades monitored simultaneously. Finally, the simulation and physical test results indicate that the proposed method exhibits high reconstruction accuracy, reliability, and anti-noise abilities. [ABSTRACT FROM AUTHOR]

In this survey paper, we review recent advances of compressed sensing applied to systems and control. Compressed sensing has been actively researched in the field of signal processing and machine learning. More recently, the method has been applied to systems and control problems, such as sparse feedback gain design, reduced-order control, and maximum hands-off control. This paper introduces these important applications of compressed sensing to systems and control. MATLAB programs for the numerical examples shown in this survey paper are available as supplementary materials. [ABSTRACT FROM AUTHOR]

Compressed sensing (CS) is a popular signal processing technique. However, some of its performances still need to be improved for possible secure visual applications, including the optimization of the measurement matrix, privacy assurance, and the sparse recovery performance. To this end, we present prior-based measurement matrix design and sparse recovery algorithm for privacy-assured CS scheme in the cloud. More specifically, the measurement matrix is modeled by minimizing a Frobenius difference between the identity matrix and the Gram of the weighted sensing matrix. The gradient descent method is employed to derive the prior probability-weighted measurement matrix. Further, privacy-assured CS can be achieved by using within-row permutation and chaotic matrices. Finally, we also employ the prior information to enhance the accuracy of the sparse recovery algorithm by using prior probability-weighted orthogonal matching pursuit. Theoretical analyses and simulation results demonstrate that the proposed scheme can optimize measurement matrix, achieve privacy-assured CS, and improve sparse recovery performance. [ABSTRACT FROM AUTHOR]

We introduce a lifted |$\ell _1$| (LL1) regularization framework for the recovery of sparse signals. The proposed LL1 regularization is a generalization of several popular regularization methods in the field and is motivated by recent advancements in re-weighted |$\ell _1$| approaches for sparse recovery. Through a comprehensive analysis of the relationships between existing methods, we identify two distinct types of lifting functions that guarantee equivalence to the |$\ell _0$| minimization problem, which is a key objective in sparse signal recovery. To solve the LL1 regularization problem, we propose an algorithm based on the alternating direction method of multipliers and provide proof of convergence for the unconstrained formulation. Our experiments demonstrate the improved performance of the LL1 regularization compared with state-of-the-art methods, confirming the effectiveness of our proposed framework. In conclusion, the LL1 regularization presents a promising and flexible approach to sparse signal recovery and invites further research in this area. [ABSTRACT FROM AUTHOR]

Numerous attempts have been made to develop efficient methods for solving the system of constrained nonlinear equations due to its widespread use in diverse engineering applications. In this article, we present a family of inertial‐based derivative‐free projection methods with a correction step for solving such system, in which the selection of the derivative‐free search direction is flexible. This family does not require the computation of corresponding Jacobian matrix or approximate matrix at every iteration and possess the following theoretical properties: (i) the inertial‐based corrected direction framework always automatically satisfies the sufficient descent and trust region properties without specific search directions, and is independent of any line search; (ii) the global convergence of the proposed family is proven under a weaker monotonicity condition on the mapping E$$ E $$, without the typical monotonicity or pseudo‐monotonicity assumption; (iii) the results about convergence rate of the proposed family are established under slightly stronger assumptions. Furthermore, we propose two effective inertial‐based derivative‐free projection methods, each embedding a specific search direction into the proposed family. We present preliminary numerical experiments on certain test problems to demonstrate the effectiveness and superiority of the proposed methods in comparison with existing ones. Additionally, we utilize these methods for solving sparse signal restorations and image restorations in compressive sensing applications. [ABSTRACT FROM AUTHOR]

Compressed sensing (CS) is a novel technique for MRI acceleration. The purpose of this paper was to assess the effects of CS on the radiomic features extracted from amide proton transfer‐weighted (APTw) images. Brain tumor MRI data of 40 scans were studied. Standard images using sensitivity encoding (SENSE) with an acceleration factor (AF) of 2 were used as the gold standard, and APTw images using SENSE with CS (CS‐SENSE) with an AF of 4 were assessed. Regions of interest (ROIs), including normal tissue, edema, liquefactive necrosis, and tumor, were manually drawn, and the effects of CS‐SENSE on radiomics were assessed for each ROI category. An intraclass correlation coefficient (ICC) was first calculated for each feature extracted from APTw images with SENSE and CS‐SENSE for all ROIs. Different filters were applied to the original images, and the effects of these filters on the ICCs were further compared between APTw images with SENSE and CS‐SENSE. Feature deviations were also provided for a more comprehensive evaluation of the effects of CS‐SENSE on radiomic features. The ROI‐based comparison showed that most radiomic features extracted from CS‐SENSE‐APTw images and SENSE‐APTw images had moderate or greater reliabilities (ICC ≥ 0.5) for all four ROIs and all eight image sets with different filters. Tumor showed significantly higher ICCs than normal tissue, edema, and liquefactive necrosis. Compared to the original images, filters (such as Exponential or Square) may improve the reliability of radiomic features extracted from CS‐SENSE‐APTw and SENSE‐APTw images. [ABSTRACT FROM AUTHOR]

In this paper, we propose a projection-based hybrid spectral gradient algorithm for nonlinear equations with convex constraints, which is based on a certain line search strategy. Convex combination technique is used to design a novel spectral parameter that is inspired by some classical spectral gradient methods. The search direction also meets the sufficient descent condition and trust region feature. The global convergence of the proposed algorithm has been established under reasonable assumptions. The results of the experiment demonstrate the proposed algorithm is both more promising and robust than some similar methods, and it is also capable of handling large-scale optimization problems. Furthermore, we apply it to problems involving sparse signal recovery and blurred image restoration. [ABSTRACT FROM AUTHOR]

When using untrusted third parties to compress and transmit images in real‐life scenarios, it is vital to encrypt them before compression. In order to better address the issues of low security in the original image and poor reconstruction quality of the encrypted image during compressed sensing, this paper proposes a 2D compressed sensing scheme for encrypted images based on complex‐valued measurement matrix (2DCS‐CVM). Firstly, the SHA‐256 algorithm generates keys for the hyperchaotic Lorenz system, and then the chaotic sequences are used to create encrypted images with increased security through subtractive diffusion and global permutation. Secondly, the complex‐valued Vandermonde measurement matrix is utilized for 2D compressed sensing on the encrypted image, and the two‐dimensional projected gradient with embedding decryption algorithm is used to generate recovered images with improved reconstruction performance. Finally, the measurement matrix's computational complexity and transmission bandwidth are reduced through structural sparsification with sparse random matrices. Simulation results demonstrate that this scheme offers an optimal balance between storage, computational complexity, hardware implementation, and reconstruction performance while providing excellent security and robustness. [ABSTRACT FROM AUTHOR]

AbstractMatrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special cases. In this article, we propose a general framework for dynamic matrix recovery of low-rank matrices that evolve smoothly over time. We start from the setting that the observations are independent across time, then extend to the setting that both the design matrix and noise possess certain temporal correlation via modified concentration inequalities. By pooling neighboring observations, we obtain sharp estimation error bounds of both settings, showing the influence of the underlying smoothness, the dependence and effective samples. We propose a dynamic fast iterative shrinkage-thresholding algorithm that is computationally efficient, and characterize the interplay between algorithmic and statistical convergence. Simulated and real data examples are provided to support such findings. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Cardiac CINE, a form of dynamic cardiac MRI, is indispensable in the diagnosis and treatment of heart conditions, offering detailed visualization essential for the early detection of cardiac diseases. As the demand for higher-resolution images increases, so does the volume of data requiring processing, presenting significant computational challenges that can impede the efficiency of diagnostic imaging. Our research presents an approach that takes advantage of the computational power of multiple Graphics Processing Units (GPUs) to address these challenges. GPUs are devices capable of performing large volumes of computations in a short period, and have significantly improved the cardiac MRI reconstruction process, allowing images to be produced faster. The innovation of our work resides in utilizing a multi-device system capable of processing the substantial data volumes demanded by high-resolution, five-dimensional cardiac MRI. This system surpasses the memory capacity limitations of single GPUs by partitioning large datasets into smaller, manageable segments for parallel processing, thereby preserving image integrity and accelerating reconstruction times. Utilizing OpenCL technology, our system offers adaptability and cross-platform functionality, ensuring wider applicability. The proposed multi-device approach offers an advancement in medical imaging, accelerating the reconstruction process and facilitating faster and more effective cardiac health assessment. [ABSTRACT FROM AUTHOR]

Differences between conventional sonar and Multiple-Input Multiple-Output (MIMO) sonar systems arise in achieving high angular and range resolution. MIMO sonar uses Matched Filtering (MF) with well-correlated transmitted signals to enhance spatial resolution by obtaining virtual arrays. However, imperfect correlation characteristics yield high sidelobe values, which hinder accurate target localization in underwater imagery. To address this, a Compressed Sensing (CS) method is proposed by reconstructing echo signals to suppress correlation noise between orthogonal waveforms. A shifted dictionary matrix and a deterministic Discrete Fourier Transform (DFT) measurement matrix are used to multiply received echo signals to yield compressed measurements. A sparse recovery algorithm is applied to optimize signal reconstruction before joint transmit–receive beamforming forms a 2D sonar image in the angle-range domain. Numerical simulations and lake experimental results confirm the effectiveness of the proposed method, by obtaining a lower sidelobe sonar image under sub-Nyquist sampling rates as compared with other approaches. [ABSTRACT FROM AUTHOR]

Cardiac MRI is a crucial tool for assessing congenital heart disease (CHD). However, its application remains challenging in young children when performed at 3T. The aim of this retrospective single center study was to compare a non-contrast free-breathing 2D CINE T1-weighted TFE-sequence with compressed sensing (FB 2D CINE CS T1-TFE) with 3D imaging for diagnostic accuracy of CHD, image quality, and vessel diameter measurements in sedated young children. FB 2D CINE CS T1-TFE was compared with a 3D non-contrast whole-heart sequence (3D WH) and 3D contrast-enhanced MR angiography (3D CE-MRA) at 3T in 37 CHD patients (20♂, 1.5±1.4 years). Two radiologists independently assessed image quality, type of CHD, and diagnostic confidence. Diameters and measures of contrast and sharpness of the aorta and pulmonary vessels were determined. A non-parametric multi-factorial approach was used to estimate diagnostic accuracy for the diagnosis of CHD. Linear mixed models were calculated to compare contrast and vessel sharpness. Krippendorff's alpha was determined to quantify vessel diameter agreement. FB 2D CINE CS T1-TFE was rated superior regarding image quality, diagnostic confidence, and diagnostic sensitivity for both intra- and extracardiac pathologies compared to 3D WH and 3D CE-MRA (all p<0.05). FB 2D CINE CS T1-TFE showed superior contrast and vessel sharpness (p<0.001) resulting in the highest proportion of measurable vessels (740/740; 100%), compared to 3D WH (530/620; 85.5%) and 3D CE-MRA (540/560; 96.4%). Regarding vessel diameter measurements, FB 2D CINE CS T1-TFE revealed the closest inter-reader agreement (Krippendorff's alpha: 0.94–0.96; 3D WH: 0.78–0.94; 3D CE-MRA: 0.76–0.93). FB 2D CINE CS T1-TFE demonstrates robustness at 3T and delivers high-quality diagnostic results to assess CHD in sedated young children. Its ability to function without contrast injection and respiratory compensation enhances ease of use and could encourage widespread adoption in clinical practice. [ABSTRACT FROM AUTHOR]

The improved Sparse Signal Reconstruction (SR) algorithm for Trusted Artificial Intelligence (AI) and Distributed Compressed Sensing (DCS) technology was thoroughly investigated. The study verified its effectiveness and advantages in trusted AI and DCS systems, which have significant implications for enhancing the credibility, security, and performance of signal processing and AI algorithms. The reconstruction performance was evaluated using Orthogonal Matching Pursuit (OMP), Basis Pursuit (BP), and Least Absolute Shrinkage and Selection Operator (LASSO). The analysis primarily focused on runtime, refactoring errors, and the number of successful reconstruction attempts. When K = 4, K = 6, K = 8, and K = 10, OMP outperformed BP and LASSO in terms of successful reconstructions, demonstrating better performance and higher reconstruction precision. [ABSTRACT FROM AUTHOR]

In this paper, a new Dai–Liao (DL)-type projection algorithm is presented for large-dimension nonlinear monotone problems with signal reconstruction and image recovery applications. The inspiration behind the work comes from two of the open problems propounded by Andrei (Bull Malays Math Sci Soc 34(2):319–330, 2011) involving the optimal value for the DL nonnegative parameter and the best conjugacy condition as well as the fine attributes expressed by four-term methods for unconstrained optimization. Based on the eigenvalue study of a symmetric DL-type iteration matrix, another optimal choice of the DL parameter is obtained, which is incorporated in a five-term direction scheme. Combining this with the projection method, a new DL algorithm which converges globally is developed. To implement the algorithm, a derivative-free line search mechanism is employed. Also, by conducting some numerical experiments with the new scheme and some recent DL-type methods, the efficiency of the former in solving nonlinear monotone problems as well as the ℓ 1 - n o r m regularized problems in compressed sensing is demonstrated. [ABSTRACT FROM AUTHOR]

Objectives: To explore the use of deep learning–constrained compressed sensing (DLCS) in improving image quality and acquisition time for 3D MRI of the brachial plexus. Methods: Fifty-four participants who underwent contrast-enhanced imaging and forty-one participants who underwent unenhanced imaging were included. Sensitivity encoding with an acceleration of 2 × 2 (SENSE4x), CS with an acceleration of 4 (CS4x), and DLCS with acceleration of 4 (DLCS4x) and 8 (DLCS8x) were used for MRI of the brachial plexus. Apparent signal-to-noise ratios (aSNRs), apparent contrast-to-noise ratios (aCNRs), and qualitative scores on a 4-point scale were evaluated and compared by ANOVA and the Friedman test. Interobserver agreement was evaluated by calculating the intraclass correlation coefficients. Results: DLCS4x achieved higher aSNR and aCNR than SENSE4x, CS4x, and DLCS8x (all p < 0.05). For the root segment of the brachial plexus, no statistically significant differences in the qualitative scores were found among the four sequences. For the trunk segment, DLCS4x had higher scores than SENSE4x (p = 0.04) in the contrast-enhanced group and had higher scores than SENSE4x and DLCS8x in the unenhanced group (all p < 0.05). For the divisions, cords, and branches, DLCS4x had higher scores than SENSE4x, CS4x, and DLCS8x (all p ≤ 0.01). No overt difference was found among SENSE4x, CS4x, and DLCS8x in any segment of the brachial plexus (all p > 0.05). Conclusions: In three-dimensional MRI for the brachial plexus, DLCS4x can improve image quality compared with SENSE4x and CS4x, and DLCS8x can maintain the image quality compared to SENSE4x and CS4x. Clinical relevance statement: Deep learning–constrained compressed sensing can improve the image quality or accelerate acquisition of 3D MRI of the brachial plexus, which should be benefit in evaluating the brachial plexus and its branches in clinical practice. Key Points: •Deep learning–constrained compressed sensing showed higher aSNR, aCNR, and qualitative scores for the brachial plexus than SENSE and CS at the same acceleration factor with similar scanning time. •Deep learning–constrained compressed sensing at acceleration factor of 8 had comparable aSNR, aCNR, and qualitative scores to SENSE4x and CS4x with approximately half the examination time. •Deep learning–constrained compressed sensing may be helpful in clinical practice for improving image quality and acquisition time in three-dimensional MRI of the brachial plexus. [ABSTRACT FROM AUTHOR]

Background: Although compressed sensing (CS) accelerated cine holds immense potential to replace conventional cardiovascular magnetic resonance (CMR) cine, how to use CS-based cine appropriately during clinical CMR examinations still needs exploring. Methods: A total of 104 patients (46.5 ± 17.1 years) participated in this prospective study. For each participant, a balanced steady state free precession (bSSFP) cine was acquired as a reference, followed by two CS accelerated cine sequences with identical parameters before and after contrast injection. Lastly, a CS accelerated cine sequence with an increased flip angle was obtained. We subsequently compared scanning time, image quality, and biventricular function parameters between these sequences. Results: All CS cine sequences demonstrated significantly shorter acquisition times compared to bSSFPref cine (p < 0.001). The bSSFPref cine showed higher left ventricular ejection fraction (LVEF) than all CS cine sequences (all p < 0.001), but no significant differences in LVEF were observed among the three CS cine sequences. Additionally, CS cine sequences displayed superior global image quality (p < 0.05) and fewer artifacts than bSSFPref cine (p < 0.005). Unenhanced CS cine and enhanced CS cine with increased flip angle showed higher global image quality than other cine sequences (p < 0.005). Conclusion: Single breath-hold CS cine delivers precise biventricular function parameters and offers a range of benefits including shorter scan time, better global image quality, and diminished motion artifacts. This innovative approach holds great promise in replacing conventional bSSFP cine and optimizing the CMR examination workflow. [ABSTRACT FROM AUTHOR]

Introduction: The image quality of continuously acquired free-breathing Dynamic Contrast-Enhanced (DCE) golden-angle radial Magnetic Resonance Imaging (MRI) of abdomen suffers from motion artifacts and motion-related blurring. We propose a scheme by minimizing patients' motion status from breathing as well as optimizing the acquiring parameters to improve image quality and diagnostic performance of DCE-MRI with Golden-Angle Radial Sparse Parallel (GRASP) sequence of abdomen. Methods: The optimization scheme follows two principles: (1) reduce the impact on images from unpredictable and irregulate motions during examination and (2) adjust the sequence parameters to increase the number of radial views in each partition. For the assessment of image quality, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), the severity of radial artifact, the degree of image sharpness, and a visual scoring of image quality with a 5-point scale were assessed. Results: A total of 64 patients were included in this study before (16 men, 14 women, age: 54.9 ± 17.0) and after (18 men, 16 women, age: 58.6 ± 12.6) the optimization scheme was performed. The results showed that the SNR values of right and left lobe of liver in both plain phase and arterial phase were significantly increased (All P < 0.001) after the GRASP sequence been optimized. Significant improvements in CNR values were observed in the arterial phase (All P < 0.05). The significant differences in scores at each phase for visual scoring of image quality, noise of the right and left lobe of liver, radial artifact, and sharpness indicating that the image quality was significantly improved after the optimization (All P < 0.001). Conclusion: Our study demonstrated that the optimized scheme significantly improved the image quality of liver DCE-MRI with GRASP sequence both in plain and arterial phases. The optimized scheme of GRASP sequence could be a superior alternative to conventional approach for the assessment of liver. [ABSTRACT FROM AUTHOR]

We present an integrated algorithm for high‐resolution crustal‐scale imaging utilizing long‐offset wide‐angle ocean‐bottom seismometer (OBS) data and short‐offset multichannel streamer (MCS) data. The algorithm adopts a two‐step imaging strategy, initially using the OBS data to enhance deep structure imaging and capture long‐wavelength features of the migration velocity. Subsequently, the MCS data are migrated to recover detailed short‐wavelength components and shallow structures using the migration velocity model modified by the OBS result. Both steps employ the least‐squares reverse time migration (LSRTM) method with appropriate regularization techniques. The algorithm is implemented using the Bregmanized operator splitting (BOS) approach, known for its efficiency and adaptability in handling non‐smooth regularization, such as total‐variation (TV) constraints. To improve computational efficiency, compressed sensing is employed to store incident wavefields at half their actual size and reconstruct them accurately when required. Convergence is expedited through the use of preconditioners and the Anderson acceleration method. The proposed algorithm is validated through large‐scale numerical examples, demonstrating its robustness even with an initially imprecise velocity model. Results showcase improved resolution and accuracy achieved through the integration of OBS and MCS data. This study offers a comprehensive framework for crustal‐scale imaging, addresses computational complexities, and provides enhanced imaging capabilities. Plain Language Summary: We present a method for high‐resolution crustal‐scale imaging using a combination of long‐offset wide‐angle data from stationary receivers deployed on the seafloor with short‐offset data from floating receivers. Our method is structured as a two‐step imaging algorithm that exploits the unique strengths of each data set. In the first step, the stationary recorded data is used to recover the long‐wavelength features. Subsequently, we integrate the floating receiver data with the preceding image to recover the short‐wavelength components, adding details. The efficacy of our method relies on the utilization of least‐squares reverse time migration, which is enhanced by incorporating appropriate regularization techniques. This enables us to address critical challenges such as memory overhead, convergence speed, and image stability. These key challenges are addressed by incorporating three advanced strategies: compressed sensing theory, Anderson acceleration, and total variation regularization. Accordingly, we enhance computational efficiency, expedite convergence, and elevate imaging quality, which helps provide accurate, high‐resolution images of the subsurface that facilitate better geological interpretation of deep structures and therefore improve our understanding of the target's regional geodynamic context. Moreover, this algorithm allows imaging with less initial knowledge about the image and more robustness to the frequency range. Key Points: Enhanced crustal‐scale seismic imaging from academic dataOcean bottom seismometer and multi‐channel streamer data integrationHigh‐resolution least‐squares reverse time migration [ABSTRACT FROM AUTHOR]

The complexity of modern power grids, caused by integrating renewable energy sources, especially inverter-based resources, presents a significant challenge to grid operation and planning, since linear models are unable to capture the complex nonlinear dynamics of power systems with coupled muti-scale dynamics, and it necessitate an alternative approach utilizing more advanced and data-driven algorithms to improve modeling accuracy and system optimization. This study employs the sparse identification of nonlinear dynamics method by leveraging compressed sensing and sparse modeling principles, offering robustness and the potential for generalization, allowing for identifying key dynamical features with relatively few measurements, and providing deeper theoretical understanding in the field of power system analysis. Taking advantage of the this method in recognizing the active terms (first and high order) in the system's governing equation, this paper also introduces the novel Volterra-based nonlinearity index to characterize system-level nonlinearity. The distinction of dynamics into first-order linearizable terms, second-order nonlinear dynamics, and third-order noise is adopted to clearly show the intricacy of power systems. The findings demonstrate a fundamental shift in system dynamics as power sources transit to inverter-based resources, revealing system-level (second-order) nonlinearity compared to module-level (first order) nonlinearity in conventional synchronous generators. The proposed index quantifies nonlinear-to-linear relationships, enriching our comprehension of power system behavior and offering a tool for distinguishing between different nonlinearities and visualizing their distinct patterns through the profile of the proposed index. [ABSTRACT FROM AUTHOR]

In this paper, we explore the problem of direction-of-arrival (DOA) estimation for a non-uniform linear array (NULA) under strong noise. The compressed sensing (CS)-based methods are widely used in NULA DOA estimations. However, these methods commonly rely on the tuning of parameters, which are hard to fine-tune. Additionally, these methods lack robustness under strong noise. To address these issues, this paper proposes a novel DOA estimation approach using a deep neural network (DNN) for a NULA in a low SNR. The proposed network is designed based on the denoising convolutional neural network (DnCNN) and the alternating direction method of multipliers (ADMM), which is dubbed as LDnADMM-Net. First, we construct an unfolded DNN architecture that mimics the behavior of the iterative processing of an ADMM. In this way, the parameters of an ADMM can be transformed into the network weights, and thus we can adaptively optimize these parameters through network training. Then, we employ the DnCNN to develop a denoising module (DnM) and integrate it into the unfolded DNN. Using this DnM, we can enhance the anti-noise ability of the proposed network and obtain a robust DOA estimation in a low SNR. The simulation and experimental results show that the proposed LDnADMM-Net can obtain high-accuracy and super-resolution DOA estimations for a NULA with strong robustness in a low signal-to-noise ratio (SNR). [ABSTRACT FROM AUTHOR]

Dynamic Magnetic Resonance Imaging (dMRI) is a valuable tool for understanding changes in human physiology, but its temporal and spatial resolution can be limited. Compressed sensing (CS) has been used to enhance temporal resolution by acquiring partial k-spaces of each time frame and exploiting sparsity to retain spatial resolution. Invoking CS in dMRI necessitates algorithms that can leverage both spatial sparsity within each time frame and temporal sparsity across time frames. A tensor decomposition-based multi-mode dictionary learning algorithm has been proposed to learn the spatial and temporal features of dMRI data and reconstruct it more efficiently. The extensive quantitative simulations reveal the improvement induced by the proposed method in various settings compared to state-of-the-art methods in dMRI. Further, it considerably advances reconstruction speed from trained dictionaries over the state-of-the-art, permitting faster scans catering to a larger patient group. [ABSTRACT FROM AUTHOR]

Time-modulated arrays (TMAs) have a high design degrees of freedom (DoFs) to improve radiation performance, while they are prone to failure due to their hardware characteristics. In this article, we propose a novel technique to diagnose impaired TMAs based on compressed sensing (CS). The TMA diagnosis problem is reformulated as a sparse signal recovery problem at the center frequency and sidebands. Then, a method based on the difference of convex sets theory and sequential convex programming (DCS-SCP) is developed to implement diagnosis for impaired TMAs. Using a small number of far-field measurements at the same position but different frequencies, the joint recovery of the equivalent excitations at the center frequency and sidebands is realized by a mixed $ l_{0} $ l 0 / $ l_{2} $ l 2 -norm minimization method. The numerical simulation and the successful comparison with the state-of-the-art algorithms demonstrate the superiority of the proposed methods in terms of noise robustness and diagnosis accuracy. [ABSTRACT FROM AUTHOR]

The continuous wave mud pulse transmission holds great promise for the future of downhole data communication. However, significant noise interference during the transmission process poses a formidable challenge for decoding. In particular, effectively eliminating random noise with a substantial amplitude that overlaps with the pulse signal spectrum has long been a complex issue. To address this, an enhanced integration algorithm that merges variational mode decomposition (VMD) and compressed sensing (CS) to suppress high-intensity random noise is proposed in this paper. In response to the inadequacy of manually preset parameters in VMD, which often leads to suboptimal decomposition outcomes, the gray wolf optimization algorithm is designed to obtain the optimal penalty factor and decomposition mode number in VMD. Subsequently, the optimized parameter combination decomposes the signal into a series of intrinsic modes. The mode exhibiting a stronger correlation with the original signal is retained to enhance signal sparsity, thereby fulfilling the prerequisite for compressed sensing. The signal is then observed and reconstructed using the compressed sensing method to yield the final signal. The proposed algorithm has been compared with VMD, CS, and CEEMD; the results demonstrate that the method can enhance the signal–noise ratio by up to ∼20.55 dB. Furthermore, it yields higher correlation coefficients and smaller mean square errors. Moreover, the experimental results using real field data show that the useful pulse waveforms can be recognized effectively, assisting surface workers in acquiring precise downhole information, enhancing drilling efficiency, and significantly reducing the risk of engineering accidents. [ABSTRACT FROM AUTHOR]

This paper presents a performance analysis of centralized spectrum sensing based on compressed measurements. We assume cooperative sensing, where unlicensed users individually perform compressed sensing and send their results to a fusion center, which makes the final decision about the presence or absence of a licensed user signal. Several cooperation schemes are considered, such as and-rule, or-rule, majority voting, soft equal-gain combining (EGC). The proposed analysis provides simplified closed-form expressions that calculate the required number of sensors, the required number of samples, the required compression ratio, and the required signal-to-noise ratio (SNR) as a function of the probability of detection and the probability of the false alarm of the fusion center and of the sensors. The resulting expressions are derived by exploiting some accurate approximations of the test statistics of the fusion center and of the sensors, equipped with energy detectors. The obtained results are useful, especially for a low number of sensors and low sample sizes, where conventional closed-form expressions based on the central limit theorem (CLT) fail to provide accurate approximations. The proposed analysis also allows the self-computation of the performance of each sensor and of the fusion center with reduced complexity. [ABSTRACT FROM AUTHOR]

Sparse reconstruction is an important aspect of MRI, helping to reduce acquisition time and improve spatial-temporal resolution. Popular methods are based mostly on compressed sensing (CS), which relies on the random sampling of k-space to produce incoherent (noise-like) artefacts. Due to hardware constraints, 1D Cartesian phase-encode under-sampling schemes are popular for 2D CS-MRI. However, 1D under-sampling limits 2D incoherence between measurements, yielding structured aliasing artefacts (ghosts) that may be difficult to remove assuming a 2D sparsity model. Reconstruction algorithms typically deploy direction-insensitive 2D regularisation for these direction-associated artefacts. Recognising that phase-encode artefacts can be separated into contiguous 1D signals, we develop two decoupling techniques that enable explicit 1D regularisation and leverage the excellent 1D incoherence characteristics. We also derive a combined 1D + 2D reconstruction technique that takes advantage of spatial relationships within the image. Experiments conducted on retrospectively under-sampled brain and knee data demonstrate that c ombination of the proposed 1D AliasNet modules with existing 2D deep learned (DL) recovery techniques leads to an improvement in image quality. We also find AliasNet enables a superior scaling of performance compared to increasing the size of the original 2D network layers. AliasNet therefore improves the regularisation of aliasing artefacts arising from phase-encode under-sampling, by tailoring the network architecture to account for their expected appearance. The proposed 1D + 2D approach is compatible with any existing 2D DL recovery technique deployed for this application. [ABSTRACT FROM AUTHOR]

In the face of mounting economic constraints, researchers are increasingly turning to data-driven methods for reconstructing unknown global fields from limited data. While traditional compressed sensing (CS) technology addresses this challenge, the least absolute shrinkage and selection operator algorithm within CS encounters difficulties in precisely solving basis coefficients. This challenge is exacerbated by the frequently unknown observation matrix, often necessitating optimization methods for resolution. This study introduces the CS-FNN (CS-Fully Connected Neural Network) method, leveraging neural network technology to refine CS-obtained basis coefficients. This approach proves particularly advantageous in scenarios involving custom observation points. Focused on hydrofoil pressure fields, our comparative analysis with CS-PSO (CS-Particle Swarm Optimization) covers the reconstruction accuracy, the performance in varied unsteady situations, and robustness concerning the number of truncated proper orthogonal decomposition modes, measuring point distribution, and real noise environments. Results demonstrate the superiority of CS-FNN over CS-PSO in predicting global hydrofoil pressure fields, with higher reconstruction accuracy, a more flexible arrangement of measuring points, and a balance between robustness and accuracy that meets the requirements of practical engineering. This innovative method introduces a new and effective approach for recovering high-dimensional data, presenting significant potential for practical engineering applications. [ABSTRACT FROM AUTHOR]

In this article, we consider and investigate a split convex feasibility problem involving two bounded linear operators in Hilbert spaces. We introduce a self-adaptive CQ-type algorithm by selecting the stepsize which is independent of the operator norms and establish a strong convergence result of the proposed algorithm under some mild control conditions. Moreover, we propose a self-adaptive relaxed CQ-type algorithm for solving the problem constrained by sub-level sets of convex functions. A numerical example and an application in compressed sensing are also given to illustrate the convergence behaviour of our proposed algorithms. Our results in this paper improve and generalize some existing results in the literature. [ABSTRACT FROM AUTHOR]

Hyperspectral images are usually acquired in a scanning-based way, which can cause inconvenience in some situations. In these cases, RGB image spectral super-resolution technology emerges as an alternative. However, current mainstream spectral super-resolution methods aim to generate continuous spectral information at a very narrow range, limited to the visible light range. Some researchers introduce hyperspectral images as auxiliary data. But it is usually required that the auxiliary hyperspectral images have the same spatial range as RGB images. To address this issue, a general point–surface data fusion method is designed to achieve the RGB image spectral super-resolution goal in this paper, named GRSS-Net. The proposed method utilizes hyperspectral point data as auxiliary data to provide spectral reference information. Thus, the spectral super-resolution can extend the spectral reconstruction range according to spectral data. The proposed method utilizes compressed sensing theory as a fundamental physical mechanism and then unfolds the traditional hyperspectral image reconstruction optimization problem into a deep network. Finally, a high-spatial-resolution hyperspectral image can be obtained. Thus, the proposed method combines the non-linear feature extraction ability of deep learning and the interpretability of traditional physical models simultaneously. A series of experiments demonstrates that the proposed method can effectively reconstruct spectral information in RGB images. Meanwhile, the proposed method provides a framework of spectral super-resolution for different applications. [ABSTRACT FROM AUTHOR]

As a sub-Nyquist sampling structure based on compressed sensing (CS), modulated wideband converter (MWC) was proposed to overcome the sampling rate limitation of analog-to-digital converters (ADCs) for wide spectral multiband signals. Different from ideal conditions when analyzing its theory, in practice, the MWC system is implemented with non-ideal devices. Due to this deviation between the ideal model and practical hardware, any imperfection of the analog device will lead to an imperfect signal reconstruction. Although the non-ideal factors can be compensated and calibrated, the conventional compensation and calibration methods easily introduce additional phase errors. This paper aims to evaluate the impact of those phase errors on signal reconstruction performance. We point out that phase errors deteriorate the normalized mean squared errors (NMSE) and even lead to incorrect support set recovery in serious cases. We thus propose a method using the SINC signal and DC signal to measure the MWC channel response which avoids the phase errors introduced in the compensation process. To verify this method, an MWC system and a measuring platform are implemented on hardware. The measurement results show that the recovery NMSE of − 13.09dB is achieved after being measured and compensated with an input SNR of 25.47dB. [ABSTRACT FROM AUTHOR]

Ultrasound plane-wave imaging has the advantage of high frame rate in addition to high data volume. High data sampling rates and large amounts of data storage can become bottlenecks in ultrasound system design. Although compressed sensing technology can help reduce the burden of sampling and transmission, it achieves relatively low image quality because of its reliance solely on signal sparsity. Therefore, we proposed reconstructing the ultrasound signal by applying additional prior knowledge, such as plane-wave imaging and its echo characteristics. Inspired by multi-hypothesis prediction methods in video compression coding, the plane-wave multi-hypothesis prediction compressed sensing reconstruction method was proposed to improve the accuracy of reconstructions. We applied multi-hypothesis prediction and residual reconstruction on the plane wave to enhance the quality of reconstruction and correct predicted values. Also, to acquire high-quality hypotheses, two hypothesis acquisition schemes were evaluated, constructing search windows on both preceding and subsequent frames as well as the reference frame. Compared with traditional reconstruction methods that rely on sparsity, multi-hypothesis prediction compressed sensing methods can reduce signal reconstruction errors and significantly eliminate image artifacts. Furthermore, by using improved hypotheses, signal reconstruction and image quality can be enhanced, resulting in higher contrast. Comparative simulation experimental results based on the publicly available Plane-Wave Imaging Challenge in Medical Ultrasound (PICMUS) and acoustic radiation force imaging data sets demonstrate that the proposed method outperforms other methods in both reconstruction errors and image quality. This helps to reduce the complexity of sampling and transmission of the ultrasound system. [ABSTRACT FROM AUTHOR]

We assessed the feasibility of using compressed sensing accelerated, low-velocity encoded, isotropic resolution phase contrast (CLIP) magnetic resonance angiography (MRA) for avascular trajectory planning of stereoelectroencephalography. Ten healthy subjects (1 woman and 9 men; age, 33.6 ± 9.0 years) and 20 consecutive patients (12 female patients; age, 22 ± 13.6 years) were enrolled in the present study. The healthy subjects underwent CLIP-MRA, and 3 other phase contrast MRA protocols with conventional parallel imaging (PI) acceleration, including low resolution with twofold PI (PI2), high resolution (HR) with fivefold PI (PI5), and HR-PI2. The patients underwent CLIP-MRA and computed tomography angiography (CTA). The image qualities were evaluated. The numbers and locations of trajectory–vessel conflict detected using CLIP-MRA were noted. With similar scan durations, CLIP-MRA achieved higher spatial resolution compared with low resolution with PI2 and detected significantly more branches compared with HR-PI5. With the same spatial resolution, the signal/noise and contrast/noise ratios of CLIP-MRA were higher than those with HR-PI2 with a shorter scan duration. For the 12 adult patients (10 female patients; 28.8 ± 12.7 years), CLIP-MRA had better signal/noise and contrast/noise ratios than CTA. The trajectory had required modification for 14 of the 20 patients (70%), with a proportion of trajectory modification of 10.7% (23 of 215 electrodes). The middle meningeal artery, cortical vessel, and skull vessel were the main vessels with conflict (n = 11, n = 7, and n = 5, respectively). In the present study, CLIP-MRA provided a clear cortical vascular display noninvasively without intravascular contrast and radiation. The middle meningeal artery and diploic and emissary veins were the main conflict vessels and could be clearly displayed using CLIP-MRA but not CTA. [ABSTRACT FROM AUTHOR]

Based on the convex combination technique, we propose a projection-based hybrid conjugate gradient algorithm for solving nonlinear equations with convex constraints in this paper. The conjugate parameter of the proposed algorithm is a convex combination of the modified Polak-Ribière-Polyak and Dai-Yuan type conjugate parameters, and the search direction has the sufficient descent property without the use of a line search strategy. The proposed hybrid algorithm's global convergence is established under appropriate assumptions. The numerical experiments demonstrate that the proposed algorithm is more efficient and competitive than existing methods under some benchmark test problems. Furthermore, it is also extended to solve the sparse signal and impulse noise image restoration problem that arises in compressive sensing. [ABSTRACT FROM AUTHOR]

Digital pathology refers to image-based environment in which acquisition, extraction and interpretation of pathology information is supported by computational techniques. It has a huge potential to facilitate the diagnostic process, however, big data size and necessity of large storage areas are challenging. Therefore, in this research, Compressed Sensing (CS) scheme is studied with digital pathology images in order to reduce the amount of data for reconstruction. CS requires the sparsity of signals for a successful recovery which means that different sparsifying bases can alter the final performance. Wavelet, Contourlet and Shearlet Transforms are investigated to sparsify the digital pathology images, it is seen that Contourlet Transform is superior. Alternating Direction Method of Multipliers (ADMM) is chosen for reconstruction since it is a robust and fast convex optimization method. Despite the fact that digital pathology images are less sparse than classical images, CS reconstruction is satisfactory, which emphasizes the potential of CS for digital pathology. This study can be pioneering in the field of CS with digital pathology so it can encourage further studies of CS based imaging with different type of microscopes or at different wavelengths. [ABSTRACT FROM AUTHOR]

Modern analog computing, by gaining momentum from nonvolatile resistive memory devices, deals with matrix computations. In-memory analog computing has been demonstrated for solving some basic but ordinary matrix problems in one step. Among the more complicated matrix problems, compressed sensing (CS) is a prominent example, whose recovery algorithms feature high-order matrix operations and hardware-unfriendly nonlinear functions. In light of the local competitive algorithm (LCA), here, we present a closed-loop, continuous-time resistive memory circuit for solving CS recovery in one step. Recovery of one-dimensional (1D) sparse signal and 2D compressive images has been experimentally demonstrated, showing elapsed times around few microseconds and normalized mean squared errors of 10-2. The LCA circuit is one or two orders of magnitude faster than conventional digital approaches. It also substantially outperforms other (electronic or exotically photonic) analog CS recovery methods in terms of speed, energy, and fidelity, thus representing a highly promising technology for real-time CS applications. [ABSTRACT FROM AUTHOR]

This paper proposes a Boolean network model with high dimensional chaos driving and investigates the synchronization of the chaos‐driven Boolean network with a semi‐tensor product. In order to protect the privacy and ensure the security of image transmission, the synchronization results are utilized in the image cryptosystem to achieve compression and encryption. First, the driving chaos system is coupled with multiple local systems and synchronized with the transmitted encrypted signals. Second, the Boolean network is driven and synchronized with derived chaos signals. Finally, images are encrypted and compressed with chaos‐driven Boolean network signals in the transmitter, and then decrypted and recovered with synchronized chaos and Boolean network signals in the recipient. Because of the complexities of high dimensional chaos and Boolean network, the proposed cryptosystem has good security in the secure communication and image process. [ABSTRACT FROM AUTHOR]

This study aims to reconstruct signals that are sparse with a tight frame from undersampled data by using the ℓ q -minimization method. This problem can be cast as a ℓ q -minimization problem with a tight frame subjected to an undersampled measurement with a known noise bound. We proved that if the measurement matrix satisfies the restricted isometry property with δ 2 s ≤ 1 / 2 , there exists a value q 0 such that for any q ∈ (0 , q 0 ] , any signal that is s-sparse with a tight frame can be robustly recovered to the true signal. We estimated q 0 as q 0 = 2 / 3 in the case of δ 2 s ≤ 1 / 2 and discussed that the value of q 0 can be much higher. We also showed that when δ 2 s ≤ 0.3317 , for any q ∈ (0 , 1 ] , robust recovery for signals via ℓ q -minimization holds, which is consistent with the case of ℓ q -minimization without a tight frame. [ABSTRACT FROM AUTHOR]

Wireless broadband transmission channels usually have time-domain-sparse properties, and the reconstruction of these channels using a greedy search-based orthogonal matching pursuit (OMP) algorithm can effectively improve channel estimation performance while decreasing the length of the reference signal. In this research, the improved OMP and SOMP algorithms for compressed-sensing (CS)-based channel estimation are proposed for single-carrier frequency domain equalization (SC-FDE) systems, which, in comparison with conventional algorithms, calculate the path gain after obtaining the path delay and updating the observation matrices. The reliability of the communication system is further enhanced because the channel path gain is calculated using longer observation vectors, which lowers the Cramér–Rao lower bound (CRLB) and results in better channel estimation performance. The developed method can also be applied to time-domain-synchronous OFDM (TDS-OFDM) systems, and it is applicable to the improvement of other matching pursuit algorithms. [ABSTRACT FROM AUTHOR]

We present a novel architecture for the design of single-photon detecting arrays that captures relative intensity or timing information from a scene, rather than absolute. The proposed method for capturing relative information between pixels or groups of pixels requires very little circuitry, and thus allows for a significantly higher pixel packing factor than is possible with per-pixel TDC approaches. The inherently compressive nature of the differential measurements also reduces data throughput and lends itself to physical implementations of compressed sensing, such as Haar wavelets. We demonstrate this technique for HDR imaging and LiDAR, and describe possible future applications. [ABSTRACT FROM AUTHOR]

Objectives: To evaluate the image quality and diagnostic performance of AI-assisted compressed sensing (ACS) accelerated two-dimensional fast spin-echo MRI compared with standard parallel imaging (PI) in clinical 3.0T rapid knee scans. Methods: This prospective study enrolled 130 consecutive participants between March and September 2022. The MRI scan procedure included one 8.0-min PI protocol and two ACS protocols (3.5 min and 2.0 min). Quantitative image quality assessments were performed by evaluating edge rise distance (ERD) and signal-to-noise ratio (SNR). Shapiro-Wilk tests were performed and investigated by the Friedman test and post hoc analyses. Three radiologists independently evaluated structural disorders for each participant. Fleiss κ analysis was used to compare inter-reader and inter-protocol agreements. The diagnostic performance of each protocol was investigated and compared by DeLong's test. The threshold for statistical significance was set at p < 0.05. Results: A total of 150 knee MRI examinations constituted the study cohort. For the quantitative assessment of four conventional sequences with ACS protocols, SNR improved significantly (p < 0.001), and ERD was significantly reduced or equivalent to the PI protocol. For the abnormality evaluated, the intraclass correlation coefficient ranged from moderate to substantial between readers (κ = 0.75–0.98) and between protocols (κ = 0.73–0.98). For meniscal tears, cruciate ligament tears, and cartilage defects, the diagnostic performance of ACS protocols was considered equivalent to PI protocol (Delong test, p > 0.05). Conclusions: Compared with the conventional PI acquisition, the novel ACS protocol demonstrated superior image quality and was feasible for achieving equivalent detection of structural abnormalities while reducing acquisition time by half. Clinical relevance statement: Artificial intelligence–assisted compressed sensing (ACS) providing excellent quality and a 75% reduction in scanning time presents significant clinical advantages in improving the efficiency and accessibility of knee MRI for more patients. Key Points: • The prospective multi-reader study showed no difference in diagnostic performance between parallel imaging and AI-assisted compression sensing (ACS) was found. • Reduced scan time, sharper delineation, and less noise with ACS reconstruction. • Improved efficiency of the clinical knee MRI examination by the ACS acceleration. [ABSTRACT FROM AUTHOR]

Background: Four-dimensional flow (4D flow) MRI has become a clinically utilized cardiovascular flow assessment tool. However, scans can be lengthy and may require anesthesia in younger children. Adding compressed sensing can decrease scan time, but its impact on hemodynamic data accuracy needs additional assessment. Objective: To compare 4D flow hemodynamics acquired with and without compressed sensing. Materials and methods: Twenty-seven patients (median age: 13 [IQR: 9.5] years) underwent conventional and compressed sensing cardiovascular 4D flow following informed consent. Conventional 4D flow was performed using parallel imaging and an acceleration factor of 2. Compressed sensing 4D flow was performed with an acceleration factor of 7.7. Regions of interest were placed to compare flow parameters in the ascending aorta and main pulmonary artery. Paired Student's t-tests, Wilcoxon signed-rank tests, Bland–Altman plots, and intraclass correlation coefficients were conducted. A P-value of < 0.05 was considered statistically significant. Results: Mean scan acquisition time was reduced by 59% using compressed sensing (3.4 vs. 8.2 min, P < 0.001). Flow quantification was similar for compressed sensing and conventional 4D flow for the ascending aorta net flow: 47 vs. 49 ml/beat (P = 0.28); forward flow: 49 vs. 50 ml/beat (P = 0.07), and main pulmonary artery net flow: 49 vs. 51 ml/beat (P = 0.18); forward flow: 50 vs. 55 ml/beat (P = 0.07). Peak systolic velocity was significantly underestimated by compressed sensing 4D flow in the ascending aorta: 114 vs. 128 cm/s (P < 0.001) and main pulmonary artery: 106 vs. 112 cm/s (P = 0.02). Conclusion: For both the aorta and main pulmonary artery, compressed sensing 4D flow provided equivalent net and forward flow values compared to conventional 4D flow but underestimated peak systolic velocity. By reducing scan time, compressed sensing 4D flow may decrease the need for anesthesia and increase scanner output without significantly compromising data integrity. [ABSTRACT FROM AUTHOR]

This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the ℓ 1 -synthesis basis pursuit allows for a simultaneous estimation of a coefficient representation as well as the sought-for signal. However, due to linear dependencies within redundant dictionary atoms, it might be impossible to identify a specific representation vector, although the actual signal is still successfully recovered. The present manuscript studies both estimation problems from a non-uniform, signal-dependent perspective. By utilizing recent results on the convex geometry of linear inverse problems, the sampling rates describing the phase transitions of each formulation are identified. In both cases, they are given by the conic Gaussian mean width of an ℓ 1 -descent cone that is linearly transformed by the dictionary. In general, this expression does not allow for a simple calculation by following the polarity-based approach commonly found in the literature. Hence, two upper bounds involving the sparsity structure of coefficient representations are provided: The first one is based on a local condition number and the second one on a geometric analysis that makes use of the thinness of high-dimensional polyhedral cones with not too many generators. It is furthermore revealed that both recovery problems can differ dramatically with respect to robustness to measurement noise—a fact that seems to have gone unnoticed in most of the related literature. All insights are carefully validated through numerical simulations. [ABSTRACT FROM AUTHOR]

Compressed sensing (CS) is a popular data compression theory for many computer vision tasks, but the high reconstruction complexity for images prevents it from being used in many real-world applications. Existing end-to-end learning methods achieved real time sensing but lack theory guarantee for robust reconstruction results. This paper proposes a neural network called RootsNet, which integrates the CS mechanism into the network to prevent error propagation. So, RootsNet knows what will happen if some modules in the network go wrong. It also implements real-time and successfully reconstructed extremely low measurement rates that are impossible for traditional optimization-theory-based methods. For qualitative validation, RootsNet is implemented in two real-world measurement applications, i.e., a near-field microwave imaging system and a pipeline inspection system, where RootsNet easily saves 60% more measurement time and 95% more data compared with the state-of-the-art optimization-theory-based reconstruction methods. Without losing generality, comprehensive experiments are performed on general datasets, including evaluating the key components in RootsNet, the reconstruction uncertainty, quality, and efficiency. RootsNet has the best uncertainty performance and efficiency, and achieves the best reconstruction quality under super low-measurement rates. [ABSTRACT FROM AUTHOR]

Deep Unfolding Networks (DUNs) serve as a predominant approach for Compressed Sensing (CS) reconstruction algorithms by harnessing optimization. However, a notable constraint within the DUN framework is the restriction to single-channel inputs and outputs at each stage during gradient descent computations. This constraint compels the feature maps of the proximal mapping module to undergo multi-channel to single-channel dimensionality reduction, resulting in limited feature characterization capabilities. Furthermore, most prevalent reconstruction networks rely on single-scale structures, neglecting the extraction of features from different scales, thereby impeding the overall reconstruction network's performance. To address these limitations, this paper introduces a novel CS reconstruction network termed the Multi-channel and Multi-scale Unfolding Network (MMU-Net). MMU-Net embraces a multi-channel approach, featuring the incorporation of Adap-SKConv with an attention mechanism to facilitate the exchange of information between gradient terms and enhance the feature map's characterization capacity. Moreover, a Multi-scale Block is introduced to extract multi-scale features, bolstering the network's ability to characterize and reconstruct the images. Our study extensively evaluates MMU-Net's performance across multiple benchmark datasets, including Urban100, Set11, BSD68, and the UC Merced Land Use Dataset, encompassing both natural and remote sensing images. The results of our study underscore the superior performance of MMU-Net in comparison to existing state-of-the-art CS methods. [ABSTRACT FROM AUTHOR]