Block-sparse Recovery Problem Research Articles

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.

Data-Driven Attack Detection and Identification for Cyber-Physical Systems Under Sparse Sensor Attacks

This paper studies the issues of data-driven attack detection and identification for cyber-physical systems under sparse sensor attacks. First, based on the available input and output data sets, a data-driven monitor is formulated with two objectives: attack detection and attack identification. Then, with the subspace approach, a data-driven attack detection policy is presented, wherein the attack detector is designed directly by the process data. A subspace projection-based attack identification scheme is proposed via designing a bank of projection filters to determine the locations of attacked sensors. Moreover, the sparse recovery technique is adopted to decrease the combinatorial complexity of the subspace projection based identification method. The attack identification is recast into a block-sparse recovery problem. Finally, the proposed methods are verified by the simulations on a flight vehicle system.

Fast Burst-Sparsity Learning-Based Baseline Correction (FBSL-BC) Algorithm for Signals of Analytical Instruments.

Baseline correction is a critical step for eliminating the interference of baseline drift in spectroscopic analysis. The recently proposed sparse Bayesian learning (SBL)-based method can significantly improve the baseline correction performance. However, it has at least two disadvantages: (i) it works poorly for large-scale datasets and (ii) it completely ignores the burst-sparsity structure of the sparse representation of the pure spectrum. In this paper, we present a new fast burst-sparsity learning method for baseline correction to overcome these shortcomings. The first novelty of the proposed method is to jointly adopt a down-sampling strategy and construct a multiple measurements block-sparse recovery problem with the down-sampling sequences. The down-sampling strategy can significantly reduce the dimension of the spectrum; while jointly exploiting the block sparsity among the down-sampling sequences avoids losing the information contained in the original spectrum. The second novelty of the proposed method is introducing the pattern-coupled prior into the SBL framework to characterize the inherent burst-sparsity in the sparse representation of spectrum. As illustrated in the paper, burst-sparsity commonly occurs in peak zones with more denser nonzero coefficients. Properly utilizing such burst-sparsity can further enhance the baseline correction performance. Results on both simulated and real datasets (such as FT-IR, Raman spectrum, and chromatography) verify the substantial improvement, in terms of estimation accuracy and computational complexity.

Off-Grid DOA Estimation With Mutual Coupling via Block Log-Sum Minimization and Iterative Gradient Descent

Mutual coupling (MC) effect between antennas can deteriorate the direction of arrival (DOA) estimation performance. Block sparse signal representation (BSSR) is an effective solution to mitigate the MC effect. Nevertheless, continuous angle space has to be discretized into a finite set of grid points, which lead to the grid mismatch. In this paper, we present an iterative block sparsity reconstruction algorithm for off-grid DOA estimation with MC. First, by exploiting the banded symmetric Toeplitz structure of MC matrix, a reduced BSSR model is formulated to preferably mitigate the MC effect. Then, an iterative block sparsity reconstruction algorithm with multiple measurement vectors (MMV) is proposed. Due to the NP-hard property of block l0 norm minimization, a block log-sum minimization method is developed to encourage sparsity for such a block sparse recovery problem, and a surrogate objective function is derived via the majorization-minimization approach. Finally, an iterative gradient descent algorithm is explored to refine the DOAs. Simulations verify that the proposed off-grid algorithm has robustness under limited snapshots and coherent sources.

Convergence and stability analysis of iteratively reweighted least squares for noisy block sparse recovery

This paper considers the theoretical properties of iteratively reweighted least squares algorithm for noisy block sparse recovery problem (BIRLS for short). Li et al. used numerical experiments to show the remarkable performance of BIRLS algorithm for recovering a block sparse signal in noiseless measurement case, but no convergence analysis was given. In this paper, we focus on providing convergence, convergence rate and stability analysis of BIRLS algorithm for block sparse recovery in the presence of noise. The convergence of BIRLS is proved strictly. Furthermore, when the linear measurement matrix A satisfies the block restricted isometry property (abbreviated as block RIP), we show that BIRLS algorithm is stable and give the error analysis of BIRLS algorithm. We also characterize the convergence rate of the BIRLS algorithm, which implies global linear convergence for p=1 and local super-linear convergence for 0<p<1. The simplicity of BIRLS algorithm, along with the theoretical guarantees provided in this paper, make a compelling case for its adoption as a standard tool for block sparse recovery.

Multitarget Detection in Passive MIMO Radar Using Block Sparse Recovery

In this paper, we develop a new algorithm for centralized target detection in passive MIMO radar (PMR) using sparse recovery technique. PMRs use a network of receivers and illuminators of opportunity to detect and localize targets. We consider a widely separated PMR network assuming the availability of reference channels. We first transform the collected information of all receivers to a common space and combine them to attain a unified model. The problem of target detection in the extracted model is equal to a block sparse recovery problem. Since employing the generic sparse recovery tools are impractical due to the ultra-large dimension of the sensing matrix, we exploit the structure of the involving matrices and propose a very efficient distributed algorithm which extracts all scatterers, including targets and clutter simultaneously with a unified procedure. The proposed algorithm is highly efficient, and it does not require a high bandwidth link to transfer raw data from nodes to the fusion center. Moreover, the algorithm inherently benefits from parallel processing and distributes the extensive computations among receivers. Our simulation results demonstrate that the proposed algorithm outperforms the popular PMR detection algorithm, especially in the presence of interfering targets and any strong clutter residue.

Deep Learning Based Autonomous Vehicle Super Resolution DOA Estimation for Safety Driving

In this paper, a novel system architecture including a massive multi-input multi-output (MIMO) or a reconfigurable intelligent surface (RIS) and multiple autonomous vehicles is considered in vehicle location systems. The location parameters of autonomous vehicles can be estimated based on the deep unfolding technique, which is a recent advance of deep learning. Traditional vehicle location methods such as the global position system (GPS) can only locate the target vehicles with relatively low accuracy. The super resolution cannot be achieved when two vehicles are too close, which means that the safety incidents exist when autonomous vehicles are deployed in future intelligent transportation systems (ITS). Different from the existing massive MIMO or RIS equipped with a regular array such as uniform rectangular array (URA) and uniform circular array (UCA), we exploit a massive MIMO or a RIS equipped with a conformal array extended from traditional regular array. First, the rotation from the global coordinate system to the local coordinate system is achieved based on geometric algebra. Second, 2D-DOA estimation of autonomous vehicles is modeled as a novel block sparse recovery problem. Third, the deep network architecture SBLNet is implemented to learn the nonlinear characteristic from the DOAs of autonomous vehicles and the data received by massive MIMOs or RISs. The 2D-DOA and polarization parameters can be estimated based on SBLNet with relatively low computational complexity. Simulation results demonstrate that SBLNet performs better than the state-of-the-art methods in terms of estimation accuracy and successful probability. The SBLNet is also suitable for the practical scenario considering fast moving autonomous vehicles, while, the traditional block sparse recovery methods fail in this complex scenario.

Robust Weighted Subspace Fitting for DOA Estimation via Block Sparse Recovery

In this letter, a novel robust block sparse recovery algorithm by using the weighted subspace fitting (WSF) is proposed to deal with the direction-of-arrival (DOA) problem under the condition of unknown mutual coupling. Firstly, a novel block sparse representation signal model based on the WSF is established to settle the effect of unknown mutual coupling. Then, the sparse constraint problem is investigated, and a regularization criterion between the sparsity penalty and subspace fitting error is given. Finally, the DOA estimation problem can be converted into a block sparse recovery problem. Some experimental results are carried out to prove the performance of proposed method in the case of unknown mutual coupling.

Block Bayesian matching pursuit based channel estimation for FDD massive MIMO system

Massive multi-input multi-output (MIMO) has been recognized as a key technology for 5G communication system due to the high array gain and spectral efficiency. To redeem the merits, the base station (BS) requires the accurate channel state information (CSI), which consumes large amount of pilot overhead for downlink CSI acquisition in frequency division duplex system. To address this issue, a block Bayesian matching pursuit (BBMP) based channel estimation approach is proposed, which fully exploits the common support of channels from multiple antennas at the BS. Specifically, the channel estimation problem is formulated as the block sparse recovery problem, where the prior probability for block support set is accordingly derived. Then, based on the prior knowledge and equivalent sensing matrix, a selection metric is defined to select the block index into the dominant support by exploiting the maximum likelihood criterion. Furthermore, by utilizing a matching pursuit based approach, the update criterion is derived for selection metric when the dominant support set augments with the iteration. Simulation results demonstrate that the proposed BBMP algorithm is capable to significantly reduce the pilot overhead for channel estimation and robust to the channel sparsity information.

Generalized Spatial Modulation-Based Multi-User and Signal Detection Scheme for Terrestrial Return Channel With NOMA

The terrestrial return channel provides interactive services in digital television terrestrial broadcasting systems to meet various consumers’ demands around the world. The extension of non-orthogonal multiple access and generalized spatial modulation multiple-input multiple-output to the terrestrial return channel improves both the spectral and energy efficiencies of the system, but it puts forward detection challenges. In this paper, a joint user activity and signal detection scheme based on the block-sparse compressive sensing (BS-CS) method in the terrestrial return channel is proposed, in which the generalized spatial modulation technology is used. By exploiting the structure and sparsity of the multi-user generalized spatial modulation signal, we formulate the detection problem into a block-sparse recovery problem. Then a BS-CS-based detection algorithm, enhanced structured block-sparse compressive sampling matching pursuit (ESB-CoSaMP), is proposed to detect the active users and transmitted data efficiently. Moreover, the information of active antennas at each user is exploited in ESB-CoSaMP to further improve the accuracy. Simulations show that the proposed detection scheme outperforms the conventional CS and BS-CS-based schemes.

Block-Sparse Recovery via Convex Optimization

Given a dictionary that consists of multiple blocks and a signal that lives in the range space of only a few blocks, we study the problem of finding a block-sparse representation of the signal, i.e., a representation that uses the minimum number of blocks. Motivated by signal/image processing and computer vision applications, such as face recognition, we consider the block-sparse recovery problem in the case where the number of atoms in each block is arbitrary, possibly much larger than the dimension of the underlying subspace. To find a block-sparse representation of a signal, we propose two classes of non-convex optimization programs, which aim to minimize the number of nonzero coefficient blocks and the number of nonzero reconstructed vectors from the blocks, respectively. Since both classes of problems are NP-hard, we propose convex relaxations and derive conditions under which each class of the convex programs is equivalent to the original non-convex formulation. Our conditions depend on the notions of mutual and cumulative subspace coherence of a dictionary, which are natural generalizations of existing notions of mutual and cumulative coherence. We evaluate the performance of the proposed convex programs through simulations as well as real experiments on face recognition. We show that treating the face recognition problem as a block-sparse recovery problem improves the state-of-the-art results by 10% with only 25% of the training data.