scholarly journals A New Smoothed L0 Regularization Approach for Sparse Signal Recovery

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Jianhong Xiang ◽  
Huihui Yue ◽  
Xiangjun Yin ◽  
Linyu Wang
Keyword(s):  
Signal Reconstruction ◽  
Real Data ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Signal Recovery ◽  
Sparse Signal Reconstruction ◽  
System Equation ◽  
Norm Minimization ◽  
Better Than

Sparse signal reconstruction, as the main link of compressive sensing (CS) theory, has attracted extensive attention in recent years. The essence of sparse signal reconstruction is how to recover the original signal accurately and effectively from an underdetermined linear system equation (ULSE). For this problem, we propose a new algorithm called regularization reweighted smoothed L0 norm minimization algorithm, which is simply called RRSL0 algorithm. Three innovations are made under the framework of this method: (1) a new smoothed function called compound inverse proportional function (CIPF) is proposed; (2) a new reweighted function is proposed; and (3) a mixed conjugate gradient (MCG) method is proposed. In this algorithm, the reweighted function and the new smoothed function are combined as the sparsity promoting objective, and the constraint condition y-Φx22 is taken as a deviation term. Both of them constitute an unconstrained optimization problem under the Tikhonov regularization criterion and the MCG method constructed is used to optimize the problem and realize high-precision reconstruction of sparse signals under noise conditions. Sparse signal recovery experiments on both the simulated and real data show the proposed RRSL0 algorithm performs better than other popular approaches and achieves state-of-the-art performances in signal and image processing.

scholarly journals A Reweighted Symmetric Smoothed Function Approximating L0-Norm Regularized Sparse Reconstruction Method

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 583 ◽  
Author(s):  
Jianhong Xiang ◽  
Huihui Yue ◽  
Xiangjun Yin ◽  
Guoqing Ruan
Keyword(s):  
Objective Function ◽  
Numerical Experiments ◽  
State Of The Art ◽  
Real Data ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Reconstruction Method ◽  
Norm Minimization ◽  
Noisy Conditions

Sparse-signal recovery in noisy conditions is a problem that can be solved with current compressive-sensing (CS) technology. Although current algorithms based on L 1 regularization can solve this problem, the L 1 regularization mechanism cannot promote signal sparsity under noisy conditions, resulting in low recovery accuracy. Based on this, we propose a regularized reweighted composite trigonometric smoothed L 0 -norm minimization (RRCTSL0) algorithm in this paper. The main contributions of this paper are as follows: (1) a new smoothed symmetric composite trigonometric (CT) function is proposed to fit the L 0 -norm; (2) a new reweighted function is proposed; and (3) a new L 0 regularization objective function framework is constructed based on the idea of T i k h o n o v regularization. In the new objective function framework, Contributions (1) and (2) are combined as sparsity regularization terms, and errors as deviation terms. Furthermore, the conjugate-gradient (CG) method is used to optimize the objective function, so as to achieve accurate recovery of sparse signal and image under noisy conditions. The numerical experiments on both the simulated and real data verify that the proposed algorithm is superior to other state-of-the-art algorithms, and achieves advanced performance under noisy conditions.

scholarly journals A Simple Gaussian Measurement Bound for Exact Recovery of Block-Sparse Signals

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zhi Han ◽  
Jianjun Wang ◽  
Jia Jing ◽  
Hai Zhang
Keyword(s):  
Lower Bound ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Signal Recovery ◽  
Minimization Method ◽  
Numerical Examples ◽  
Norm Minimization ◽  
Minimization Methods ◽  
Theoretical Results

We present a probabilistic analysis on conditions of the exact recovery of block-sparse signals whose nonzero elements appear in fixed blocks. We mainly derive a simple lower bound on the necessary number of Gaussian measurements for exact recovery of such block-sparse signals via the mixedl2/lq  (0<q≤1)norm minimization method. In addition, we present numerical examples to partially support the correctness of the theoretical results. The obtained results extend those known for the standardlqminimization and the mixedl2/l1minimization methods to the mixedl2/lq  (0<q≤1)minimization method in the context of block-sparse signal recovery.

Smoothing inertial neurodynamic approach for sparse signal reconstruction via Lp-norm minimization

2021 ◽  
Vol 140 ◽  
pp. 100-112
Author(s):  
You Zhao ◽  
Xiaofeng Liao ◽  
Xing He ◽  
Rongqiang Tang ◽  
Weiwei Deng
Keyword(s):  
Signal Reconstruction ◽  
Sparse Signal ◽  
Sparse Signal Reconstruction ◽  
Lp Norm ◽  
Norm Minimization

scholarly journals Sparse Signal Recovery for Direction-of-Arrival Estimation Based on Source Signal Subspace

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Lin ◽  
Jiying Liu ◽  
Meihua Xie ◽  
Jubo Zhu
Keyword(s):  
Computational Cost ◽  
Real Data ◽  
Direction Of Arrival ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Signal Subspace ◽  
Second Order Cone ◽  
Source Signal ◽  
Improved Accuracy

After establishing the sparse representation of the source signal subspace, we propose a new method to estimate the direction of arrival (DOA) by solving anℓ1-norm minimization for sparse signal recovery of the source powers. Second-order cone programming is applied to reformulate this optimization problem, and it is solved effectively by employing the interior point method. Due to the keeping of the signal subspace and the discarding of the noise subspace, the proposed method is more robust to noise than many other sparsity-based methods. The real data tests and the numerical simulations demonstrate that the proposed method has improved accuracy and robustness to noise, and it is not sensitive to the knowledge about the number of sources. We discuss the computational cost of our method theoretically, and the experiment results verify the computational effectiveness.

Block Sparse Signal Reconstruction Using Block-Sparse Adaptive Filtering Algorithms

2016 ◽  
Vol 20 (7) ◽  
pp. 1119-1126 ◽  
Author(s):  
Chen Ye ◽  
◽  
Guan Gui ◽  
Shin-ya Matsushita ◽  
Li Xu ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Adaptive Filtering ◽  
Large Scale ◽  
Block Structure ◽  
Signal Reconstruction ◽  
Lms Algorithm ◽  
Sparse Signal ◽  
Sparse Signals ◽  
Filtering Algorithms ◽  
Sparse Signal Reconstruction

Sparse signal reconstruction (SSR) problems based on compressive sensing (CS) arise in a broad range of application fields. Among these are the so-called “block-structured” or “block sparse” signals with nonzero atoms occurring in clusters that occur frequently in natural signals. To make block-structured sparsity use more explicit, many block-structure-based SSR algorithms, such as convex optimization and greedy pursuit, have been developed. Convex optimization algorithms usually pose a heavy computational burden, while greedy pursuit algorithms are overly sensitive to ambient interferences, so these two types of block-structure-based SSR algorithms may not be suited for solving large-scale problems in strong interference scenarios. Sparse adaptive filtering algorithms have recently been shown to solve large-scale CS problems effectively for conventional vector sparse signals. Encouraged by these facts, we propose two novel block-structure-based sparse adaptive filtering algorithms, i.e., the “block zero attracting least mean square” (BZA-LMS) algorithm and the “block&ell;0-norm LMS” (BL0-LMS) algorithm, to exploit their potential performance gain. Experimental results presented demonstrate the validity and applicability of these proposed algorithms.

scholarly journals Sparse Signal Recovery via ECME Thresholding Pursuits

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Heping Song ◽  
Guoli Wang
Keyword(s):  
Optimization Problems ◽  
Greedy Algorithms ◽  
Experimental Studies ◽  
Superior Performance ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Signal Recovery ◽  
Support Set ◽  
Reconstructed Signal

The emerging theory of compressive sensing (CS) provides a new sparse signal processing paradigm for reconstructing sparse signals from the undersampled linear measurements. Recently, numerous algorithms have been developed to solve convex optimization problems for CS sparse signal recovery. However, in some certain circumstances, greedy algorithms exhibit superior performance than convex methods. This paper is a followup to the recent paper of Wang and Yin (2010), who refine BP reconstructions via iterative support detection (ISD). The heuristic idea of ISD was applied to greedy algorithms. We developed two approaches for accelerating the ECME iteration. The described algorithms, named ECME thresholding pursuits (EMTP), introduced two greedy strategies that each iteration detects a support setIby thresholding the result of the ECME iteration and estimates the reconstructed signal by solving a truncated least-squares problem on the support setI. Two effective support detection strategies are devised for the sparse signals with components having a fast decaying distribution of nonzero components. The experimental studies are presented to demonstrate that EMTP offers an appealing alternative to state-of-the-art algorithms for sparse signal recovery.

scholarly journals High-Resolution ISAR Imaging Based on Improved Sparse Signal Recovery Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Junjie Feng ◽  
Yinan Sun ◽  
XiuXia Ji
Keyword(s):  
High Resolution ◽  
Optimization Problem ◽  
Signal Reconstruction ◽  
Variable Parameter ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Loop Structure ◽  
Recovery Algorithm ◽  
Isar Imaging

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.

scholarly journals A Note on Block-Sparse Signal Recovery with Coherent Tight Frames

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yao Wang ◽  
Jianjun Wang ◽  
Zongben Xu
Keyword(s):  
Sufficient Conditions ◽  
Tight Frame ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Tight Frames ◽  
Signal Recovery ◽  
Analysis Method ◽  
Measurement Matrix ◽  
Undersampled Data

This note discusses the recovery of signals from undersampled data in the situation that such signals are nearly block sparse in terms of an overcomplete and coherent tight frameD. By introducing the notion of blockD-restricted isometry property (D-RIP), we establish several sufficient conditions for the proposed mixedl2/l1-analysis method to guarantee stable recovery of nearly block-sparse signals in terms ofD. One of the main results of this note shows that if the measurement matrix satisfies the blockD-RIP with constantsδk<0.307, then the signals which are nearly blockk-sparse in terms ofDcan be stably recovered via mixedl2/l1-analysis in the presence of noise.

scholarly journals Backtracking based Joint-Sparse Signal Recovery for Distributed Compressive Sensing

2019 ◽  
Vol 9 (2) ◽  
pp. 3919-3922
Keyword(s):  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Reconstruction Method ◽  
Joint Sparsity ◽  
Joint Reconstruction ◽  
Distributed Compressive Sensing ◽  
Efficient Recovery

In Distributed Compressive Sensing (DCS), the Joint Sparsity Model (JSM) refers to an ensemble of signals being jointly sparse. In [4], a joint reconstruction scheme was proposed using a single linear program. However, for reconstruction of any individual sparse signal using that scheme, the computational complexity is high. In this paper, we propose a dual-sparse signal reconstruction method. In the proposed method, if one signal is known apriori, then any other signal in the ensemble can be efficiently estimated using the proposed method, exploiting the dual-sparsity. Simulation results show that the proposed method provides fast and efficient recovery.

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