Sparse Signal Recovery Research Articles

New scheme of cooperative compressed spectrum sensing

Abstract This study addresses key challenges in sparse signal recovery and compressed spectrum sensing (CSS), focusing on low signal-to-noise ratios (SNR), and the computational complexity of cooperative systems. Motivated by the need for faster and more accurate recovery techniques, we first investigate and generalize the Reduced-Set Matching Pursuit (RMP) algorithm, which overcomes the speed and accuracy limitations of conventional greedy algorithms. Secondly, we propose a novel spatial averaging technique that enhances detection performance by exploiting data from multiple users to counteract low SNR. Lastly, we integrate cooperation into CSS, further improving the detection capabilities during the recovery process. Compared to existing techniques like Joint Sparse Recovery (JSR) and CoSaMP, which face computational and accuracy constraints in real-time applications, the RMP algorithm, combined with the Virtual method (data transformation) and AND fusion rule, delivers superior performance than JSR methods. Moreover, spatial averaging significantly increases the probability of cooperative detection Q d , with SNR increasing linearly by a factor of L − 1 per channel. The results are validated through the implementation of SDR. These findings demonstrate the potential of RMP and cooperation to overcome current limitations in CSS, advancing the state-of-the-art in spectrum sensing for collaborative networks.

Frame-based block sparse compressed sensing via l2/l1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_2/l_1$$\\end{document}-synthesis

In this paper, we consider the frame-based block sparse signal recovery via a l2/l1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_2/l_1$$\\end{document}-synthesis method. A new kind of null space property based on the given dictionary D(block D-NSP) is proposed. It is proved that sensing matrices satisfying the block D-NSP is not just a sufficient and necessary condition for the l2/l1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_2/l_1$$\\end{document}-synthesis method to exactly recover signals that are block sparse in frame D, but also a sufficient and necessary condition for the l2/l1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_2/l_1$$\\end{document}-synthesis to stably recover signals which are block-compressible in frame D. To the best of our knowledge, this new property is the first sufficient and necessary condition for successful signal recovery via the l2/l1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_2/l_1$$\\end{document}-synthesis. In addition, we also characterize the theoretical performance of recovering signals via the l2/l1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_2/l_1$$\\end{document}-synthesis in the case of the measurements are disturbed.

Non-signal components minimization for sparse signal recovery

Sparse signal recovery is a challenging task. This paper focuses on the technique of non-signal components minimization for recovering the latent sparsest signal behind observations from two viewpoints: minimizing the residual subject to the sparsity level and minimizing the sparsity subject to the residual constraint. A successive sparsity increment method is proposed to address these two closely related tasks. This method yields two algorithms: SINSM for residual minimization and SISP for sparsity minimization. Additionally, an improved accelerated proximal gradient algorithm is provided to solve each non-signal components minimization problem penalized by the residual. The convergence of the improved algorithm is guaranteed. Numerical experiments demonstrate the superior performance of SINSM and SISP on both synthetic and real-world data.

Iteratively reweighted least squares for block sparse signal recovery with unconstrained l2,p minimization

In this paper, we study an unconstrained [Formula: see text] minimization and its associated iteratively reweighted least squares algorithm (UBIRLS) for recovering block sparse signals. Wang et al. [Y. Wang, J. Wang and Z. Xu, On recovery of block-sparse signals via mixed [Formula: see text] [Formula: see text] norm minimization, EURASIP J. Adv. Signal Process. 2013(76) (2013) 76] have used numerical experiments to show the remarkable performance of UBIRLS algorithm for recovering a block sparse signal, but no theoretical analysis such as convergence and convergence rate analysis of UBIRLS algorithm was given. We focus on providing convergence and convergence rate analysis of UBIRLS algorithm for block sparse recovery problem. First, the convergence of UBIRLS is proved strictly. Second, based on the block restricted isometry property (block RIP) of linear measurement matrix [Formula: see text], we give the error bound analysis of the UBIRLS algorithm. Lastly, we also characterize the local convergence behavior of the UBIRLS algorithm. The simplicity of UBIRLS algorithm, along with the theoretical guarantees provided in this paper, will make a compelling case for its adoption as a standard tool for block sparse recovery.

Distributed ISAR imaging based on convolution and total variation reweighted l1 regularization

ABSTRACT Distributed Inverse Synthetic Aperture Radar (ISAR) systems employ multiple spatially separated radars to observe a target, with the potential to enhance radar imaging azimuth resolution and gather more target information. Due to the existence of gaps in the observation angles of each radars, the coherence between pulses of radar echo is disrupted during fusion imaging, making it challenging for the Range-Doppler (RD) algorithm to achieve well-focused images. This paper proposes an imaging method based on sparse signal recovery (SSR), using the reweighted l 1 norm with convolution and total variation as regularization terms. This approach not only yields well-focused ISAR images but also better preserves the overall target information compared to other methods, while also exhibiting excellent noise resistance. In addition, the alternating direction method of multipliers (ADMM) algorithm is utilized for the solution to reduce computational complexity. Simulation and measured data verify the effectiveness of the proposed method.

LRPS‐GCN: A millimeter wave sparse imaging algorithm based on graph signal

AbstractAiming at the problems of slow speed and poor accuracy of traditional millimeter wave sparse imaging, a sparse imaging algorithm based on graph convolution model is proposed from the perspective of sparse signal recovery. The graph signal model is constructed by combining the low‐rank and piecewise smoothing(LRPS) regular terms, based on which the proximal operator is replaced by the denoising graph convolution network, and the graph convolution sparse reconstruction network LRPS‐GCN is constructed, and the recovered target image is obtained by iterating with the optimal non‐linear sparse variation. For the proposed algorithm, simulation experiments are carried out using synthetic datasets under different target densities, iteration times and noise environments, and compared with the traditional graph signal reconstruction algorithm and the deep compressed sensing reconstruction algorithm, and then use the measured data with varying degrees of sparsity to validate. The experimental results show that the reconstructed images by this algorithm have better performance in terms of normalised mean square error, target to background ratio, reconstruction time and memory usage.

Uniform RIP analysis for the [formula omitted]-[formula omitted] minimization

This paper presents a uniform restricted isometry property (RIP) analysis of the ℓp−ωℓq minimization method for the recovery of sparse signals in both noiseless and noisy scenarios. The analysis is primarily based on a crucial sparse representation for any given signals. Moreover, we propose an effective algorithm for solving the ℓp−ωℓq minimization problem. The performance of this algorithm is validated through extensive numerical experiments on synthetic data, ECG signals, and grayscale images.

Shuffled multi-channel sparse signal recovery

Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless vital sign monitoring may be severely affected by mismatched sample-channel assignments. To address this issue systematically, we frame it as a signal reconstruction problem where correspondences between samples and channels are lost. Assuming a sensing matrix for the signals, we show the problem’s equivalence to a highly structured unlabeled sensing problem and establish conditions for unique recovery. This is crucial since existing unlabeled sensing theory is inapplicable and results for reconstructing shuffled multi-channel signals do not yet exist. Our results extend to continuous-time sparse signals, and we derive conditions for reconstructing shuffled sparse signals. For the two-channel case, we provide a first reconstruction method, which combines sparse signal recovery with robust linear regression, outperforming existing unlabeled sensing methods in numerical experiments. Additionally, we showcase its effectiveness in a real-world application involving calcium imaging traces. Our theory marks a significant initial step in addressing this challenging signal reconstruction problem, with potential extensions to diverse signal representations encountered in real-world problems with imprecise measurement or channel assignment.

DNN-Sparse Bayesian Learning (SBL) based Sparse Signal Recovery in Compressed Sensing

DNN-Sparse Bayesian Learning (SBL) based Sparse Signal Recovery in Compressed Sensing

A sampling greedy average regularized Kaczmarz method for tensor recovery

AbstractRecently, a regularized Kaczmarz method has been proposed to solve tensor recovery problems. In this article, we propose a sampling greedy average regularized Kaczmarz method. This method can be viewed as a block or mini‐batch version of the regularized Kaczmarz method, which is based on averaging several regularized Kaczmarz steps with a constant or adaptive extrapolated step size. Also, it is equipped with a sampling greedy strategy to select the working tensor slices from the sensing tensor. We prove that our new method converges linearly in expectation and show that the sampling greedy strategy can exhibit an accelerated convergence rate compared to the random sampling strategy. Numerical experiments are carried out to show the feasibility and efficiency of our new method on various signal/image recovery problems, including sparse signal recovery, image inpainting, and image deconvolution.

Direction-of-Arrival Estimation via Sparse Bayesian Learning Exploiting Hierarchical Priors with Low Complexity.

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

Analysis of T-Orthogonal greedy algorithm in noisy measurement

We define the Tikhonov Orthogonal Greedy algorithm (T-OGA), a variant of the orthogonal greedy algorithm, to study the recovery of sparse signals from noisy measurements. We establish sufficient conditions for T-OGA to recover sparse signals via restricted isometry property (RIP) inherited from frames. We introduce various concepts such as match matrix, match vector, and residue vector to execute T-OGA. Various technical lemmas have been established to prove our main theorem. In the execution of T-OGA, we employ Tikhonov regularization with regularization parameter λ to solve the minimization problem for the N-sparse solution. In our main result, we proved that if a frame satisfies the RIP of order N + 1 with isometry constant τ and (τ+λ)<13N , then T-OGA can recover every N-sparse signal in the atmost N iterations.

A novel predefined-time neurodynamic approach for mixed variational inequality problems and applications

In this paper, we propose a novel neurodynamic approach with predefined-time stability that offers a solution to address mixed variational inequality problems. Our approach introduces an adjustable time parameter, thereby enhancing flexibility and applicability compared to conventional fixed-time stability methods. By satisfying certain conditions, the proposed approach is capable of converging to a unique solution within a predefined-time, which sets it apart from fixed-time stability and finite-time stability approaches. Furthermore, our approach can be extended to address a wide range of mathematical optimization problems, including variational inequalities, nonlinear complementarity problems, sparse signal recovery problems, and nash equilibria seeking problems in noncooperative games. We provide numerical simulations to validate the theoretical derivation and showcase the effectiveness and feasibility of our proposed method.

Binary Least Squares: An Algorithm for Binary Sparse Signal Recovery

Binary Least Squares: An Algorithm for Binary Sparse Signal Recovery

Compressed sensing for rapid tabletop X-ray absorption spectroscopy

X-ray Absorption Fine Structure (XAFS) spectroscopy is an analytical technique of chemical insight. Improvements to this technique are continuously carried out for reduction of the acquisition time and increasing the resolution, especially for studying operando processes. The accurate reconstruction of XAFS signals requires that the collected data are noise-free to extract elemental structure information in post-processing. A novel approach to rapid sampling (encoded measurement) is validated conceptually. The technique relies on sparse signal recovery, i.e. using compressed sensing to reconstruct under-sampled signals. The proof of concept is demonstrated by using a python code to reconstruct under-sampled XAFS spectra. A case study of transition metal samples and their oxides is considered for this purpose. The results demonstrate a robust recovery of chemical information from a 30% sampled signal for the near-edge region analysis and from a 45% sampled signal for extended-edge region analysis. The application of this procedure is important for demonstrating the feasibility of tabletop operation using laboratory X-ray sources which are not continuously tunable.

Sufficient condition based on nearly optimal order RIC for IHT algorithm

Iterative hard thresholding (IHT) is one class of sparse signal recovery algorithms widely used in compressed sensing. The well-known restricted isometry constant (RIC) is one of the most popular frameworks used to ensure the convergence of recovery algorithms. In previous literature, sufficient conditions to guarantee the recovery performance of the IHT algorithm have usually been established based on RICs with orders 3 s and 2 s , while no such condition in terms of RIC with order less than 2 s has been reported yet. In this study, based on the theoretical optimal step-length, we develop the RIC condition γ < ( 5 − 1 ) / 8 ≈ 0.1545 for successful recovery via the IHT algorithm. Here, γ = δ s if s is an even number, otherwise γ = δ s + 1 . To the best of our knowledge, this is the first result based on RIC with nearly optimal order for the IHT algorithm.

MsDC-DEQ-Net: Deep Equilibrium Model (DEQ) with Multiscale Dilated Convolution for Image Compressive Sensing (CS)

Compressive sensing (CS) is a technique that enables the recovery of sparse signals using fewer measurements than traditional sampling methods. To address the computational challenges of CS reconstruction, our objective is to develop an interpretable and concise neural network model for reconstructing natural images using CS. We achieve this by mapping one step of the iterative shrinkage thresholding algorithm (ISTA) to a deep network block, representing one iteration of ISTA. To enhance learning ability and incorporate structural diversity, we integrate aggregated residual transformations (ResNeXt) and squeeze-and-excitation mechanisms into the ISTA block. This block serves as a deep equilibrium layer connected to a semi-tensor product network for convenient sampling and providing an initial reconstruction. The resulting model, called MsDC-DEQ-Net, exhibits competitive performance compared to state-of-the-art network-based methods. It significantly reduces storage requirements compared to deep unrolling methods, using only one iteration block instead of multiple iterations. Unlike deep unrolling models, MsDC-DEQ-Net can be iteratively used, gradually improving reconstruction accuracy while considering computation tradeoffs. Additionally, the model benefits from multiscale dilated convolutions, further enhancing performance.

A low-complexity DOA estimation algorithm using UAMP with Bernoulli-Gaussian prior

In this paper, we design a low-complexity direction-of-arrival (DOA) estimation algorithm based on the unitary approximate message passing (UAMP) and Bernoulli-Gaussian (BG) prior. We first show that the estimation of DOA can be transferred into a sparse signal recovery problem, where we turn to UAMP with damping technique to solve this problem. Furthermore, we assume the BG prior on the sparse vector to be estimated, resulting in the fast estimation of the positions of non-zero elements. Moreover, expectation maximum (EM) is leveraged to automatically learn the BG parameters. Compared to the state-of-the-art UAMP-based algorithm with sparse Bayesian learning (SBL), the proposed approach can achieve the same DOA mean square error (MSE) performance with a much faster convergence speed.

Efficient Recovery of Sparse Graph Signals from Graph Filter Outputs

Efficient Recovery of Sparse Graph Signals from Graph Filter Outputs

Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown Borders

Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown Borders