Sparse Signal Recovery Algorithm Research Articles

Multiple Line Outage Detection in Power Systems by Sparse Recovery Using Transient Data

Fast and accurate transmission line outage detection can help the central control unit to respond rapidly to better maintain the security and reliability of power systems. It is especially critical in the situation of multiple line outages which is more likely to trigger cascading failures. In this article, we investigate the problem of multiple line outage detection through sparse representation based on the transient dynamics captured by Phasor Measurement Units (PMUs). An accumulation-based method is proposed to reduce the noise interference. By introducing an adaptive threshold selection rule, a modified sparse signal recovery algorithm is proposed to improve the performance of multiple line outage detection. Furthermore, an event-triggered mechanism is presented to reduce the computation burden. Finally, numerical experiments based on the IEEE Standard Test Bus System are conducted to illustrate the effectiveness of our method.

Adaptive support-driven Bayesian reweighted algorithm for sparse signal recovery

This paper presents an adaptive support-driven Bayesian reweighted algorithm based on shrinkage thresholding, for large-scale sparse signal recovery. The proposed algorithm is based on the widely used sparse Bayesian learning (SBL) methods, which relies on parameterized prior. SBL leads to a nonconvex optimization problem that encourages model with few nonzero coefficients. In SBL, sparse signal recovery problems can be solved by a reweighted $$\ell _1$$ -regularization algorithm. However, this algorithm is expensive in computation and memory, especially for large-scale problem. To alleviate this problem, we proposed a restart strategy leading to the adaptive support estimate, which reduces the computational burden and memory simultaneously. Numerical experiments demonstrate the effectiveness and computational advantages of the proposed algorithm.

Analysis of the modified multiple OLS (mbm$^2$OLS) algorithm for sparse signal recovery with noise

Analysis of the modified multiple OLS (mbm$^2$OLS) algorithm for sparse signal recovery with noise

High‐Resolution ISAR Imaging Based on Improved Sparse Signal Recovery Algorithm

In order to solve the problem of high‐resolution ISAR imaging under the condition of finite pulses, an improved smoothed L0 norm (SL0) sparse signal reconstruction ISAR imaging algorithm is proposed. Firstly, the ISAR imaging is transformed into the optimization problem of minimum L0 norm. Secondly, a single‐loop structure is used instead of two loop layers in SL0 algorithm which increases the searching density of variable parameter to ensure the recovery accuracy. Finally, the compared step is added to ensure the optimization solution along the steepest descent gradient direction. The experimental results show that the proposed algorithm has better imaging effect.

A new conjugate gradient hard thresholding pursuit algorithm for sparse signal recovery

The hard thresholding pursuit algorithm in compressive sensing theory is widely used to recover sparse signal because of its good convergence. In this paper, combined with the conjugate gradient method, a modified conjugate gradient hard thresholding pursuit algorithm is proposed to accelerate the convergence speed of the traditional hard thresholding algorithm, and the theoretical proof of the convergence of the algorithm is given. Finally, numerical experiments such as signal recovery and image reconstruction demonstrate the validity of the proposed algorithm.

ISAR Imaging Based on Multiple Measurement Vector Model Sparse Signal Recovery Algorithm

A multiple measurement vector (MMV) model blocks sparse signal recovery. ISAR imaging algorithm is proposed to improve ISAR imaging quality. Firstly, the sparse imaging model is built, and block sparse signal recovery algorithm-based MMV model is applied to ISAR imaging. Then, a negative exponential function is proposed to approximately block L0 norm. The optimization solution of smoothed function is obtained by constructing a decreasing sequence. Finally, the correction steps are added to ensure the optimal solution of the block sparse signal along the fastest descent direction. Several simulations and real data simulation experiments verify the proposed algorithm has advantages in imaging time and quality.

Distributed ISAR Imaging of Rotating Target Based on Homotopy L1L0 Method

The distributed ISAR technique can form multiple virtual equivalent sensors to observe the target from multiple observation angles, and can obtain more spatial sampling data at the same time than monostatic ISAR, so it has the potential to increase the cross-range resolution. In this paper, sparse signal recovery algorithms are proposed to obtain the cross-range image of the distributed ISAR when the conventional Fourier transform imaging method is not applicable due to (1) nonuniform rotation of the target (2) large echo gap and (3) low echo SNR. After obtaining the distributed ISAR echoes, the range migration of the scatterer in each equivalent sensor is analyzed, and a cross-range phase that causes a positioning error is compensated. Then, the sparse representation of the echo in each range bin is given and the homotopy L1L0 (HL1L0) method is introduced. Singular value decomposition (SVD) is used to improve the robustness of the algorithm. Simulation results show that the sparse recovery algorithms can achieve high cross-range resolution, and HL1L0 method is better than orthogonal matching pursuit (OMP) and smoothed L0 (SL0) under different echo gaps and SNRs according to the four proposed evaluation criteria. Real data experiment verifies the advantage of the distributed ISAR and the effectiveness of the proposed method.

Reconstruction of 2D Seismic Wavefields from Nonuniformly Sampled Sources

In a 3D seismic survey, the source sampling in a regular grid is commonly limited by economic costs, geological constraints, and environmental challenges. This non-uniform sampling cannot be ignored since the lack of regularity leads to incomplete seismic data with missing 2D wavefields. Notice that the postprocessing tasks have been developed under the assumption that 3D seismic data are obtained from a regular sampling. Therefore, signal recovery from incomplete data becomes a crucial step in the seismic imaging processing flow. In this work, we propose a pre-processing step that includes the nonuniformly acquired wavefields in a finer regular grid, such that shot gathers are stacked considering the actual spatial location of the sources. Then, based on the 3D curvelet transform, a sparse signal recovery algorithm that considers an interpolation operator is employed in order to reconstruct the missing wavefields in a regular grid. The performance of the proposed seismic reconstruction approach is evaluated on a real data set.

Newton-Step-Based Hard Thresholding Algorithms for Sparse Signal Recovery

Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for nonlinear optimization problems. In this paper, we propose the so-called Newton-step-based iterative hard thresholding (NSIHT) and the Newton-step-based hard thresholding pursuit (NSHTP) algorithms for sparse signal recovery and signal approximation. Different from the traditional iterative hard thresholding (IHT) and hard thresholding pursuit (HTP), the proposed algorithms adopts the Newton-like search direction instead of the steepest descent direction. A theoretical analysis for the proposed algorithms is carried out, and some sufficient conditions for the guaranteed success of sparse signal recovery via these algorithms are established. Our results are shown under the restricted isometry property which is one of the standard assumptions widely used in the field of compressed sensing and signal approximation. The empirical results obtained from synthetic data recovery indicate that the proposed algorithms are efficient signal recovery methods. The numerical stability of our algorithms in terms of the residual reduction is also investigated through simulations.

Greedy Algorithms for Sparse and Positive Signal Recovery Based on Bit-Wise MAP Detection

We propose a novel greedy algorithm to recover a sparse signal from a small number of noisy measurements. In the proposed method, a new support index is identified for each iteration based on bit-wise maximum a posteriori (B-MAP) detection. This is an optimal in the sense of recovering one of the remaining support indices, provided that all the detected indices during the previous iterations are correct. Despite its optimality, it is unpractical due to an expensive complexity as the computation of the maximization metric (i.e., a posteriori probability of each remaining support) requires the marginalization of high-dimensional sparse vector. We address this problem by presenting a good proxy (named B-MAP proxy) of the maximization metric. The proposed B-MAP proxy is accurate enough to accomplish our purpose (i.e., finding a maximum index during iterations) and simply evaluated via simple vector correlations as in conventional orthogonal-matching-pursuit (OMP). We verify that, when non-zero values of a sparse signal follow a probability distribution with non-zero mean, the proposed B-MAP attains a higher recovery accuracy than the existing methods as OMP and MAP-OMP, while having the same complexity. Subsequently, advanced greedy algorithms, based on B-MAP proxy, are constructed using the idea of compressive-sampling-matching-pursuit (CoSaMP) and subspace-pursuit (SP). Simulations demonstrate that B-MAP can outperform OMP and MAP-OMP under the frameworks of the advanced greedy algorithms. We remark that the performance gains of the proposed algorithms are larger as the means of non-zero values of a random sparse signal become far from zero.

Bayesian Compressive Sampling Based Wideband Spectrum Sensing in Cognitive Radio Network using Wavelet Transform

This paper deals with the implementation of sub Nyquist sampling for the efficient wideband spectrum sensing in cognitive radio network. Cognitive radio is a very promising technology in the field of wireless communication which has drastically changed the spectral dynamics through the opportunistic utilization of frequency band by the secondary users when it is not utilized by the primary users. The complexity of spectral detection strategy is reduced using the compressive sensing method. Bayesian technique is utilized in the compressive sampling to deal with uncertainty of the process and increase the speed of detection. This technique recovers the wideband signals even with few measurements via Laplace prior and Toeplitz matrix. Sparse signal recovery algorithm is used for the extraction of primary user frequency location. The condition of the detection of primary user even in the low regulated transmission from unlicensed user is been resolved in this paper through Wavelet transform. This approach enables the evaluation of all possible hypotheses simultaneously in the global optimization framework. Simulation analysis is performed to verify the effectiveness of the proposed technique over the cognitive radio network.

A modified multiple OLS (m2OLS) algorithm for signal recovery in compressive sensing

Orthogonal least square (OLS) is an important sparse signal recovery algorithm in compressive sensing, which enjoys superior probability of success over other well known recovery algorithms under conditions of correlated measurement matrices. Multiple OLS (mOLS) is a recently proposed improved version of OLS which selects multiple candidates per iteration by generalizing the greedy selection principle used in OLS and enjoys faster convergence than OLS. In this paper, we present a refined version of the mOLS algorithm where at each step of iteration, we first preselect a submatrix of the measurement matrix suitably and then apply the mOLS computations to the chosen submatrix. Since mOLS now works only on a submatrix and not on the overall matrix, computations reduce drastically. Convergence of the algorithm, however, requires to ensure passage of true candidates through the two stages of preselection and mOLS based identification successively. This paper presents convergence conditions for both noisy and noise free signal models. The proposed algorithm enjoys faster convergence properties similar to mOLS, at a much reduced computational complexity.

VLSI Architecture for Enhanced Approximate Message Passing Algorithm

Compressed sensing (CS) enables the reconstruction of sparse signals from a small number of linear measurements. However, sparse signal recovery algorithms require significant computational effort, even for problems of moderate size, and make their hardware realization a highly challenging task. In this paper, we present a novel architecture for the reconstruction of the sparse signal using the recently proposed Enhanced Approximate Message Passing (EAMP) algorithm. The EAMP algorithm shows better performance in terms of convergence rate and sparsity measurement trade-off as compared to AMP, IST and IHT techniques. The execution time of the proposed design has been reduced by maximizing parallelism with an appropriate level of unfolding. It receives CS measurements (y) and the number of non-zero elements (K) in the input vector from the encoder. Depending on the value of K, one sensing matrix (Φ j ) is selected from the code book Φ. The reconstruction algorithm (EAMP) recovers the input vector (s) by using y and Φ. Bitonic sorting has been used to identify the thresholding value in the EAMP algorithm. The proposed architecture for EAMP algorithm has been synthesized using Synopsys design compiler with 65 nm technology CMOS standard cell libraries. It occupies 719.15 KGE and consumes 315.5 mW power at a frequency of 400 MHz. It is suitable for any arbitrary sparsity-based signal restoration and CS problems.

Modal regression based greedy algorithm for robust sparse signal recovery, clustering and classification

Greedy algorithm (GA) is an efficient sparse representation framework with numerous applications in machine learning and computer vision. However, conventional GA methods may fail when applied to grossly corrupted data because they iteratively estimate the sparse signal using least squares regression, which is sensitive to gross corruption and outliers. In this paper, we propose a modal regression based greedy algorithm referred as MROMP (modal regression based orthogonal matching pursuit) to robustly learn the sparse signal from corrupted measurements. Unlike previous GA methods, MROMP is based on sparse modal regression, which has decent robustness to heavy-tailed noise and outliers. To efficiently optimize MROMP, we devise two half-quadratic based algorithms with guaranteed convergence. Our another two contributions are leveraging MROMP to develop a robust subspace clustering method to cluster data lying in a union of subspaces, and a robust pattern classification method to recognize data into the class that they belong to, respectively. The experimental results on both simulated and real datasets demonstrate the efficacy and robustness of MROMP for sparse signal recovery, data clustering and classification, especially for grossly corrupted data.

Bayesian Matching Pursuit: A Finite-Alphabet Sparse Signal Recovery Algorithm for Quantized Compressive Sensing

In this letter, we consider the problem of detecting finite-alphabet sparse signals from noisy and coarsely quantized measurements. To solve this problem, we propose a greedy sparse signal detection algorithm referred to as Bayesian matching pursuit (BMP). The key idea of BMP is to identify the non-zero elements of a sparse signal that produce the largest a posteriori probabilities in an iterative fashion. Our simulation results show that the BMP algorithm outperforms the existing sparse signal reconstruction algorithms in terms of frame error rates even with a significantly reduced computational complexity.

Structured Bayesian learning for recovery of clustered sparse signal

This paper considers the problem of recovering sparse signals with cluster structure of unknown sizes and locations. A hybrid prior is proposed by introducing a local continuity indicator, which adaptively imposes cluster information on the sparse coefficients according to the inherent data structure. The local continuity indicator flexibly switches the prior for a sparse coefficient between a fully pattern-coupled one and an independent one, so that the estimation of the sparse coefficient can selectively use the statistical information of its neighbors. Variational Bayesian inference is used to estimate the hidden variables based on the constructed probabilistic modeling. Numerical results of comprehensive simulations and real data experiments demonstrate that the proposed algorithm can effectively avoid the problem of structural mismatch and outperform other recently reported clustered sparse signal recovery algorithms in noisy environments.

Block-sparse signal recovery based on orthogonal matching pursuit via stage-wise weak selection

For recovering the block-sparse signal with unknown block structures, this paper presents a Block Stage-wise Weak Orthogonal Matching Pursuit (BSWOMP) algorithm. Which partitions the original signal into different groups or segments and conducts the selection for these groups separately using weak selection method to update reconstructing support set. And it proves that the Restricted Isometry Property (RIP) of BSWOMP algorithm is slack than Stage-wise Weak Orthogonal Matching Pursuit (SWOMP) algorithm and Block Orthogonal Matching Pursuit (BOMP) algorithm, this means BSWOMP algorithm generates better convergence than traditional sparse signal recovery algorithm. To further analysis of the performance of BSWOMP, the effectiveness of this algorithm is demonstrated by simulations. Experiments results show that the proposed algorithm effectively selects the nonzero elements of the block-sparse signal by a threshold, and compared with the traditional algorithms, BSWOMP algorithm has higher recovering stability, expedites the approximate conjugate gradient update step and brings an evident performance improvement and application prospect.

Evolutionary algorithms for sparse signal reconstruction

This study includes an evolutionary algorithm technique for sparse signal reconstruction in compressive sensing. In general, l1 minimization and greedy algorithms are used to reconstruct sparse signals. In addition to these methods, recently, heuristic algorithms have begun to be used to reconstruct sparse signals. Heuristic algorithms are used in the field of compressive sensing by creating a hybrid structure with other methods or by optimizing the problem of sparse signal reconstruction on its own. This proposed method for evolutionary algorithms has a strategy similar to the sparse signal recovery method of greedy algorithms used in compressive sensing. In addition, this method has been applied for genetic and differential evolution algorithms. Firstly, the reconstruction performance of genetic and differential evolution algorithms is compared among each other. And then, the reconstruction performance of them is compared with l1 minimization method and greedy approaches. As a result from these studies, the proposed method for genetic and differential evolution algorithms can be used as the sparse signal recovery algorithm.

Construction of highly redundant incoherent unit norm tight frames as a union of orthonormal bases

Unit norm tight frames are useful in providing stable reconstruction. Incoherence, restricted isometry property and statistical restricted isometry property of a frame provide performance guarantees of sparse signal recovery algorithms in compressed sensing. Equiangular tight frames, mutually unbiased bases and chirp matrices are well known incoherent unit norm tight frames that exhibit near optimal sparse recovery guarantees. The dimension of frame elements belongs to some particular family of numbers and the number of elements in these frames is in the order of square of the dimension of the underlying space. In the present work, we construct incoherent unit norm tight frames for more general dimensions with higher redundancy than these frames. One of the important features of our construction is that it produces incoherent unit norm tight frames that are a union of orthonormal bases. In addition, the incoherent unit norm tight frames that we construct possess the statistical restricted isometry property and statistical incoherence property. As a result they exhibit near optimal theoretical guarantees in recovering sparse signals obtained from a generic random signal model. Using simulations, we demonstrate the efficacy of the constructed tight frames as good candidates for recovering sparse signals as against partial Fourier matrices and with existing constructions of incoherent unit norm tight frames.

Adaptive algorithm for sparse signal recovery

The development of compressive sensing in recent years has given much attention to sparse signal recovery. In sparse signal recovery, spike and slab priors are playing a key role in inducing sparsity. The use of such priors, however, results in non-convex and mixed integer programming problems. Most of the existing algorithms to solve non-convex and mixed integer programming problems involve either simplifying assumptions, relaxations or high computational expenses. In this paper, we propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the suggested non-convex and mixed integer programming problem. The algorithm is based on the one-to-one mapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternating direction method of multipliers to recover the signal corresponding to the updated support. Moreover, as opposed to the competing “adaptive sparsity matching pursuit” and “alternating direction method of multipliers” methods our algorithm can solve non-convex problems directly. Experiments on synthetic data and real-world images demonstrated that the proposed AADMM algorithm provides superior performance and is computationally cheaper than the recently developed iterative convex refinement (ICR) and adaptive matching pursuit (AMP) algorithms.