A Regularized Weighted Smoothed L0 Norm Minimization Method for Underdetermined Blind Source Separation

Abstract

Compressed sensing (CS) theory has attracted widespread attention in recent years and has been widely used in signal and image processing, such as underdetermined blind source separation (UBSS), magnetic resonance imaging (MRI), etc. As the main link of CS, the goal of sparse signal reconstruction is how to recover accurately and effectively the original signal from an underdetermined linear system of equations (ULSE). For this problem, we propose a new algorithm called the weighted regularized smoothed L0-norm minimization algorithm (WReSL0). Under the framework of this algorithm, we have done three things: (1) proposed a new smoothed function called the compound inverse proportional function (CIPF); (2) proposed a new weighted function; and (3) a new regularization form is derived and constructed. In this algorithm, the weighted function and the new smoothed function are combined as the sparsity-promoting object, and a new regularization form is derived and constructed to enhance de-noising performance. Performance simulation experiments on both the real signal and real images show that the proposed WReSL0 algorithm outperforms other popular approaches, such as SL0, BPDN, NSL0, and Lp-RLSand achieves better performances when it is used for UBSS.

A New Regularized Reconstruction Algorithm Based on Compressed Sensing for the Sparse Underdetermined Problem and Applications of One-Dimensional and Two-Dimensional Signal Recovery

“…In order to verify the performance of the proposed algorithm, we compare the popular WReSL0 [19] and ReSL0 [5] algorithms with the proposed CReSL0 algorithm in reconstructing a one-dimensional signal and two-dimensional image by the MATLAB simulation platform. The MATLAB simulation platform runs on a 64-bit Intel i5-4210 CPU@1.7GHz processor and Windows 8 system.…”

“…However, the ReSL0 algorithm uses the Gauss approximation function and the steepest descent optimization method of the SL0 algorithm. On the one hand, through our research and investigation, we find that many approximation functions are better than the Gauss function, such as the approximation function in [19]; on the other hand, although the steepest descent optimization method adopted by ReSL0 does not require the accurate initial value, the optimization algorithm itself has drawbacks. In the early stage of the algorithm, the steepest descent method does have the best approach; however, in the later stage of optimization, there will be a jagged optimization path, and the convergence becomes very slow.…”

“…In the section above, it can be clearly seen that the ReSL0 algorithm mainly changes the original projection part of the basis of the SL0 algorithm, but the optimization method still chooses the steepest descent method, and the approximation function is also the Gauss function. In this paper, the CIPF function in [19] will be selected as follows:…”

“…The well-known Newton method has second-order convergence, but the Newton method requires a more accurate initial value, and it is not easy to get a perfect initial value. For this reason, we add the combined optimization method of the steepest descent method and Newton method to the ReSL0 algorithm and select the approximation function as used in [19]. Thus, the combined-optimization ReSL0 algorithm is proposed in this paper, which is called the CReSL0 algorithm.…”

A Novel Image-Restoration Method Based on High-Order Total Variation Regularization Term

“…In the field of electronics and information, signal processing is a hot research topic, and as a special signal, the study of image has attracted the attention of scholars all over the world [1][2][3]. In image processing, image restoration is one of the most important issues and this issue has received extensive attention in the past few decades [4][5][6][7][8][9][10][11]. Image restoration is a technology that uses degraded images and some prior information to restore and reconstruct clear images, to improve image quality.…”