A New Smoothed L0 Regularization Approach for Sparse Signal Recovery. (17th July 2019)

• Record Type: Journal Article
• Authors: Xiang, Jianhong; Yue, Huihui; Yin, Xiangjun; Wang, Linyu
• Other Names: Ogryczak Wlodzimierz Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2019(2019)
• Publication Date: 2019-07-17
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2019/1978154
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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 smoothedL 0 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 conditiony - Φ x 2 2 is taken as a deviation term. Both of them constitute an unconstrained optimization problem under theT i k h o n o v 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.