Block-sparse Signals Research Articles

The stable reconstruction of strongly-decaying block sparse signals

The stable reconstruction of strongly-decaying block sparse signals

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.

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.

Joint block sparse signal recovery-based active user detection in 5G cloud radio access networks

Joint block sparse signal recovery-based active user detection in 5G cloud radio access networks

High-order block RIP for nonconvex block-sparse compressed sensing

Abstract This paper concentrates on the recovery of block-sparse signals, which are not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear measurements. We establish high-order sufficient conditions based on block RIP, which could ensure the exact recovery of every block s-sparse signal in the noiseless case via mixed l 2 / l p {l_{2}/l_{p}} minimization method, and the stable and robust recovery in the case that signals are not accurately block-sparse in the presence of noise. Additionally, a lower bound on necessary number of random Gaussian measurements is gained for the condition to be true with overwhelming probability. Furthermore, a series of numerical experiments are conducted to demonstrate the performance of the mixed l 2 / l p {l_{2}/l_{p}} minimization. To the best of the authors’ knowledge, the recovery guarantees established in this paper are superior to those currently available.

Nonzero Degree-Based Multiobjective Cooperative Coevolutionary for Block Sparse Recovery

Block sparse signals have the characteristics of nonzero values concentrated as blocks. Therefore, block sparse recovery requires recovering the original signal from the observed signal and the measurement matrix, where the recovered error should be small and the signal satisfies the block sparsity. In this paper, block sparse recovery is solved as a multiobjective problem (MOP) and the recovery error, sparsity, and the block number of the recovered signal are considered as the conflicting objectives. Furthermore, the dimensionality of real block sparse signals is often too large, which increases the difficulty of recovery. Cooperative coevolutionary (CC) can effectively alleviate the curse of dimensionality in block sparse recovery. In addition, block sparsity causes zero and nonzero variables in the signal to form natural clusters, which is similar to the decomposition and cooperation of subproblems in CC. Therefore, CC is used in the algorithm to solve the block sparse MOP and decomposes the original problem into different subproblems. Each subproblem has a defined nonzero degree that can be combined with the proposed adaptive operator to adaptively adjust the way of generating new solutions of subproblem, which encourages the complete solution to have block sparsity. For the increased number of function evaluations (FEs) caused by the decomposition, a new list-inquiry evaluation is designed to avoid repeated evaluation. Finally, the experimental results on simulated data and real data have demonstrated the effectiveness of the proposed algorithm.

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

Block sparse signal recovery via minimizing the block [formula omitted]-ratio sparsity

In this paper, we propose a method for block sparse signal recovery that minimizes the block q-ratio sparsity ‖z‖2,1/‖z‖2,qqq−1 with q∈[0,∞]. For the case of 1<q≤∞, we present the theoretical analyses and the computing algorithms for both cases of the ℓ2-bounded and ℓ2,∞-bounded noises. The corresponding unconstrained model is also investigated. Its superior performance in block sparse signal reconstruction is demonstrated by numerical experiments.

RBDL: Robust block-Structured dictionary learning for block sparse representation

Dictionary learning methods have been extensively used in different types of image and signal processing tasks. In a number of applications, the collected data/signal may have a multi-subspace structure and be perturbed with outliers. These motivate the use of robust and block-sparse signal representations. In this paper, a new algorithm for learning a block-structured dictionary in the presence of outliers is proposed. It is based on α−divergence and has the advantage of tolerating the presence of outliers. A block coordinate descent approach is adopted to obtain simple closed-form solutions for both the sparse coding and dictionary update stages. Finally, experimental results illustrating the superiority of the proposed method over some state-of-the-art dictionary learning methods, are provided.

Covariance-Free Variational Bayesian Learning for Correlated Block Sparse Signals

We consider the problem of estimating channel in massive machine type communication (mMTC) systems. The sparse device activity in a mMTC system makes the channel block-sparse, with intra-block correlation. Block-sparse Bayesian learning (B-SBL) is a powerful framework for estimating such signals. The existing B-SBL algorithms become computationally expensive for high-dimensional problems, which is common in mMTC systems. This is because of large number of devices in a mMTC system, they invert a large-dimensional matrix to calculate the covariance matrix. To address this problem, we exploit variational Bayesian inference, and design a novel covariance-free variational B-SBL algorithm which inverts multiple small-sized block matrices, instead of inverting a complete big-sized matrix. The complexity is further reduced by avoiding explicit computation of the covariance matrix. The proposed algorithm, instead of performing costly matrix inversions, solves multiple linear systems to calculate an unbiased estimate of the posterior statistics. The proposed algorithm is numerically shown to estimate the mMTC channel with a much lesser complexity, and that too without compromising the reconstruction performance.

Block-sparse recovery and rank minimization using a weighted l_{p}-l_{q} model

In this paper, we study a nonconvex, nonsmooth, and non-Lipschitz weighted l_{p}-l_{q} (0< pleq 1, 1< qleq 2; 0leq alpha leq 1) norm as a nonconvex metric to recover block-sparse signals and rank-minimization problems. Using block-RIP and matrix-RIP conditions, we obtain exact recovery results for block-sparse signals and rank minimization. We also obtain the theoretical bound for the block-sparse signals and rank minimization when measurements are degraded by noise.

Block Sparse Bayesian Learning Based Joint User Activity Detection and Channel Estimation in Grant-Free MIMO-NOMA

In the massive machine type of communication (mMTC), grant-free non-orthogonal multiple access (NOMA) is receiving more and more attention because it can skip the complex grant process to allocate non-orthogonal resources to serve more users. To address the limited wireless resources and substantial connection challenges, combining grant-free NOMA and multiple-input multiple-output (MIMO) is crucial to further improve the system’s capacity. In the grant-free MIMO-NOMA system, the base station should obtain the relevant information of the user before data detection. Thus, user activity detection (UAD) and channel estimation (CE) are two problems that should be solved urgently. In this paper, we fully consider the sparse characteristics of signals and the spatial correlation between multiple antennas in the grant-free MIMO-NOMA system. Then, we propose a spatial correlation block sparse Bayesian learning (SC-BSBL) algorithm to address the joint UAD and CE problems. First, by fully mining the block sparsity of signals in the grant-free MIMO-NOMA system, we model the joint UAD and CE problem as a three-dimensional block sparse signal recovery problem. Second, we derive the cost function based on the hierarchical Bayesian theory and spatial correlation. Finally, to estimate the channel and the set of active users, we optimize the cost function with fast marginal likelihood maximization. The simulation results indicate that, compared with the existing algorithms, SC-BSBL can always fully use the signal sparsity and spatial correlation to accurately complete UAD and CE under various user activation probabilities, SNRs, and the number of antennas. The normalized mean square error of CE can be reduced to 0.01, and the UAD error rate can be less than 10−5.

One-bit block sparse signal recovery via nonconvex ℓ2/ℓp(0&lt;p&lt;1)-minimization

One-bit compressed sensing (1-bit CS) shows that a sparse signal can exactly be recovered from extremely quantized linear measurements which just catch their signs. While in many applications, real-world signals also exhibit additional structures aside from standard sparsity, such as block-sparsity. We proposed a nonconvex ℓ2 / ℓp ( 0 < p < 1 ) -minimization model. Using the best approximation, covering number, and packing number, we obtain a weak condition to reconstruct block-sparse signals with high probability. And the lower bound of the required number of measurements is lower than some existing 1-bit CS methods. At last, we propose a block adaptive binary iteration thresholding algorithm to recover ℓ2 / ℓp effectively block sparse signals. The algorithm can be used without knowing the sparsity of the underlying signal. Several simulations are conducted to reveal the superiority of our methods to existing approaches, which expose the advantage of 1-bit CS in the reconstruction of block-sparse signals.

DOA Estimation for Massive MIMO Systems with Unknown Mutual Coupling Based on Block Sparse Bayesian Learning.

Obtaining accurate angle parameters using direction-of-arrival (DOA) estimation algorithms is crucial for acquiring channel state information (CSI) in massive multiple-input multiple-output (MIMO) systems. However, the performance of the existing algorithms deteriorates severely due to mutual coupling between antenna elements in practical engineering. Therefore, for solving the array mutual coupling, the array output signal vector is modeled by mutual coupling coefficients and the DOA estimation problem is transformed into block sparse signal reconstruction and parameter optimization in this paper. Then, a novel sparse Bayesian learning (SBL)-based algorithm is proposed, in which the expectation-maximum (EM) algorithm is used to estimate the unknown parameters iteratively, and the convergence speed of the algorithm is enhanced by utilizing the approximate approximation. Moreover, considering the off-grid error caused by discretization processes, the grid refinement is carried out using the polynomial roots to realize the dynamic update of the grid points, so as to improve the DOA estimation accuracy. Simulation results show that compared with the existing algorithms, the proposed algorithm is more robust to mutual coupling and off-grid error and can obtain better estimation performance.

Application of Intelligent Signal Reflection in the Communication Model of an Electronic Controller

This paper analyses the automatic control effect of an electronic controller, combined with artificial intelligence technology in order to improve the automatic control of an electronic controller. In order to improve the automatic control effect of the electronic controller, a novel centralized intelligent reflective surface-assisted millimeter-wave computational imaging scheme based on pixel block division and block sparse signal recovery is proposed in this paper. Meanwhile, this paper proposes a fast block-sparse Bayesian learning algorithm. It combines the GAMP algorithm with machine learning, so it can achieve similar performance with much lower computational complexity than the traditional block sparse Bayesian learning algorithm. The simulation clustering study shows that the electronic controller automation system based on artificial intelligence technology proposed in this paper can effectively improve the control effect of the electronic controller.

Phase retrieval for block sparsity based on adaptive coupled variational Bayesian learning

Phase retrieval (PR) of block-sparse signals is a new branch of sparse PR that causes rising research, which focusses with methods owing a high successful rate. However, the recovery performances of existing methods for block sparsity are usually unfit for large-scale problems with unacceptable compute complexity. We derive an algorithm for PR of block sparsity via variational Bayesian learning with expectation maximisation to mitigate this drawback. In the proposed algorithm, the block-sparse structure is modelled by the hierarchical constructional priors with a novel adaptive coupled pattern, which provides a strong relationship between the neighbour blocks. Simulations indicate that the proposed algorithm outperforms the existing methods in success rate, noise-robustness, and signal detection rate in large-scale cases with acceptable computation complexity.

Demixing Sines and Spikes Using Multiple Measurement Vectors

We address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the measurements can be modeled as the sum of a spectrally sparse and a block-sparse signal known as outlier. Our aim is to demix the two components and for this purpose, we design a convex problem whose objective function promotes both of the structures. Using the Positive Trigonometric Polynomials (PTP) theory, we reformulate the dual problem as a Semidefinite Program (SDP). Our theoretical results state that for a fixed number of measurements N and constant number of outliers, up to O(N) spectral lines can be recovered using our SDP problem as long as a minimum frequency separation condition is satisfied. Our simulation results also show that increasing the number of samples per measurement vectors reduces the minimum required frequency separation for successful recovery.

Distributed ranking-based resource allocation for sporadic M2M communication

This work proposes a novel scheme for distributed ranking-based and contention-free resource allocation in large-scale machine-to-machine (M2M) communication networks. We partition a network of N devices into disjoint clusters based on service type, and assign to each cluster a cluster-specific signature for active cluster members to indicate their active status. The devices in each cluster are totally ordered in some a priori-known manner, which gives rise to an active ranking of active cluster members. In order to tackle complexity issues in large-scale M2M networks with a massive number of devices, we propose a distributed resource allocation scheme using the framework of compressed sensing (CS), which mainly consists of three phases: (i) In a full-duplex acquisition phase, the devices transmit their cluster-specific signatures simultaneously and the network activation pattern is collected in a distributed manner. (ii) The base station detects the active clusters and the number of active devices per cluster using block sketching, and allocates resources to each active cluster accordingly. (iii) Each active device determines its active ranking in the cluster and accesses a specific resource according to the ranking position. By exploiting the sparsity in the activation pattern of the M2M devices, the proposed scheme is formulated as a CS support recovery problem for a particular binary block-sparse signal xin {mathbb{B}}^N – with block sparsity K_{B} and in-block sparsity K_{I} over block size d. Our analysis shows that the proposed scheme efficiently reduces the signature length to mathcal {O}(max {K_{B}log N, K_{B}K_{I}log d}) and achieves less computational complexity of mathcal {O}(dK_{I}^{2}+frac{N}{d}log N) compared with standard CS algorithms. Moreover, numerical results suggest strong robustness of the proposed scheme under noisy conditions.

Phase retrieval for signals with block sparsity using BOMP: Algorithms and recovery guarantees

Phase retrieval (PR) from the magnitude-only measurements is a challenging problem that has attracted researchers in many scientific fields regarding the loss of phase information. However, PR for a block-sparse signal with non-zero elements present in several blocks has only a few appropriate methods that are not desirable in large-scale problems. This paper focuses on improving the adaptive capacity of PR of block sparsity for large-scale cases. Two practical greedy PR algorithms are proposed. The first is based on block orthogonal matching pursuit (BOMP) called BOMP-coordinate descent (CD). The other one invokes a tree search strategy of multipath matching pursuit (MMP), termed BMMP-CD, to promote the chance to the optimum. Theoretical conditions of BOMP-CD and BMMP-CD to select the correct index show the advantages of the proposed algorithms. Simulations show that the BOMP-CD is faster, while the recovery probability of BMMP-CD surpasses the compared counterparts.

Nonnegative block-sparse Bayesian learning algorithm for EEG brain source localization

Localizing electrical sources on the cortex surface from scalp recorded electroencephalogram (EEG) is challenging, due to ill-posed problem, noises/artifacts contamination, etc. Applying sparse Bayesian learning (SBL) in this field can automatically give sparse solution to ill-posed problem, while most of the SBL-based algorithms require precise or estimated version of noise statistics information. As EEG signals are more likely to stem from locally synchronized neural masses, modeling source block-sparsity on the cortex surface would bring benefits. In this paper, we develop an EEG brain source localization algorithm in SBL framework, with innovative modeling at sensor level as well as source level. For sensor-level modeling, the distribution of sample covariance matrix of multi-electrode measurements is considered, to circumvent the requirement of noise covariance matrix information. The innovation of source-level modeling is that, with block-sparsity prior used, the block-sparse signal reconstruction problem is transformed to an atom-sparse one, in which variance parameters of brain regions are to be estimated. As these parameters are nonnegative, their priors are modeled by nonnegative Gaussian, which was neglected by previous studies, and ultimately a nonnegative block-SBL (NNBSBL) algorithm is proposed in expectation–maximization (EM) approach. Simulations demonstrate that the proposed NNBSBL algorithm has excellent performance in variations of source number, source locations, homoscedastic/heteroscedastic noises, signal-to-noise ratio (SNR), and number of samples, compared to benchmark and state-of-the-art algorithms. The performance of the proposed algorithm is also evaluated through real P300 EEG data, which is proved consistent with the conclusions of P300 source locations in literature.