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 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 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.

NonConvex Iteratively Reweighted Least Square Optimization in Compressive Sensing

2011 ◽  
Vol 341-342 ◽  
pp. 629-633
Author(s):  
Madhuparna Chakraborty ◽  
Alaka Barik ◽  
Ravinder Nath ◽  
Victor Dutta
Keyword(s):  
Computer Simulation ◽  
Compressive Sensing ◽  
Least Square ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Reconstruction Method ◽  
Least Square Approach ◽  
Simulation Results ◽  
Regularization Strategy

In this paper, we study a method for sparse signal recovery with the help of iteratively reweighted least square approach, which in many situations outperforms other reconstruction method mentioned in literature in a way that comparatively fewer measurements are needed for exact recovery. The algorithm given involves solving a sequence of weighted minimization for nonconvex problems where the weights for the next iteration are determined from the value of current solution. We present a number of experiments demonstrating the performance of the algorithm. The performance of the algorithm is studied via computer simulation for different number of measurements, and degree of sparsity. Also the simulation results show that improvement is achieved by incorporating regularization strategy.

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.

Sparse signal recovery with prior information by iterative reweighted least squares algorithm

2018 ◽  
Vol 26 (2) ◽  
pp. 171-184 ◽  
Author(s):  
Nianci Feng ◽  
Jianjun Wang ◽  
Wendong Wang
Keyword(s):  
Least Squares ◽  
Numerical Experiments ◽  
Prior Information ◽  
Regularization Parameter ◽  
Convergence Result ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Recovery Performance ◽  
Iterative Reweighted Least Squares

AbstractIn this paper, the iterative reweighted least squares (IRLS) algorithm for sparse signal recovery with partially known support is studied. We establish a theoretical analysis of the IRLS algorithm by incorporating some known part of support information as a prior, and obtain the error estimate and convergence result of this algorithm. Our results show that the error bound depends on the best {(s+k)}-term approximation and the regularization parameter λ, and convergence result depends only on the regularization parameter λ. Finally, a series of numerical experiments are carried out to demonstrate the effectiveness of the algorithm for sparse signal recovery with partially known support, which shows that an appropriate q ({0<q<1}) can lead to a better recovery performance than that of the case {q=1}.

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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