Sparse Signal Recovery Using Iterative Proximal Projection

• Published in: IEEE transactions on signal processing Vol. 66; no. 4; pp. 879 - 894
• Main Authors: Ghayem, Fateme, Sadeghi, Mostafa, Babaie-Zadeh, Massoud, Chatterjee, Saikat, Skoglund, Mikael, Jutten, Christian
• Format: Journal Article
• Language: English
• Published: IEEE 15.02.2018; Institute of Electrical and Electronics Engineers
• Subjects: Acceleration; compressed sensing; Convergence; Cost function; Engineering Sciences; Iterative algorithms; iterative sparsification-projection; Minimization; proximal splitting algorithms; Signal and Image processing; Signal processing algorithms; SL0; Sparse signal recovery; proximal splitting algorithms; Index Terms—Sparse signal recovery; iterative sparsification-projection; compressed sensing; SL0
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2017.2778695

This paper is concerned with designing efficient algorithms for recovering sparse signals from noisy underdetermined measurements. More precisely, we consider minimization of a nonsmooth and nonconvex sparsity promoting function subject to an error constraint. To solve this problem, we use an alternating minimization penalty method, which ends up with an iterative proximal-projection approach. Furthermore, inspired by accelerated gradient schemes for solving convex problems, we equip the obtained algorithm with a so-called extrapolation step to boost its performance. Additionally, we prove its convergence to a critical point. Our extensive simulations on synthetic as well as real data verify that the proposed algorithm considerably outperforms some well-known and recently proposed algorithms.