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Research articles

ScienceAsia (): 311-318 |doi: 10.2306/scienceasia1513-1874...311

An Inverse Matrix-Free Proximal Point Algorithm for Compressive Sensing

Hongchun Suna,*, Min Sunb,c, Bohan Zhangd

ABSTRACT:     In recent years, the compressive sensing (CS) has received considerable attention in signal processing and statistical inference. The classical proximal point algorithm (PPA) for some reformulations of CS often involves an inverse matrix at each iteration, which usually requires expensive computation if high dimensional variables are considered. Our contribution in this paper is to propose a novelly inverse matrix-free PPA to solve CS for the first time. More specifically, we first establish some equivalent reformulations of CS, which are smooth and convex. Based on these equivalent reformations, a new proximal point algorithm is proposed to solve CS, whose inverse matrix can be removed by choosing some special parameter. Thus we get an inverse matrix-free PPA, which is implementable for large scale CS. Global convergence of the new PPA and its inverse matrix-free version is established. Comparative numerical results are presented, which substantiate the efficacy and validity of the inverse matrix-free PPA for solving some sparse signal recovery problems.

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a School of Mathematics and Statistics, Linyi University, Shandong, Linyi, 276005, P. R. China
b School of Mathematics and Statistics, Zaozhuang University, Shandong, Zaozhuang, 277160, P. R. China
c School of Management, Qufu Normal University, Shandong, Rizhao, 276826, P. R. China
d School of Information Science and Engineering, Jinan University, Shandong, Jinan, 250022, P. R. China

* Corresponding author, E-mail: hcsun68@126.com

Received 1 Jun 2018, Accepted 26 Aug 2018