Sparse Recovery Conditions and Performance Bounds for -Minimization

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

3 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)5014-5028
Journal / PublicationIEEE Transactions on Signal Processing
Volume66
Issue number19
Online published2 Aug 2018
Publication statusPublished - 1 Oct 2018

Abstract

In sparse recovery, a sparse signal x N with K nonzero entries is to be reconstructedfrom a compressed measurement y = Ax with A M×N (M < N). The p (0 p < 1) pseudonorm has been found to be a sparsity inducing function superior tothe 1 norm, and the nullspace constant (NSC) and restricted isometry constant (RIC) have been used askey notions in the performance analyses of the corresponding p-minimization. In this paper, we study sparserecovery conditions and performance bounds for the p-minimization. We devise a new NSC upper bound thatoutperforms the state-of-the-art result. Based on the improved NSC upper bound, we provide a new RIC upper bound dependent on the sparsity level K as a sufficient condition for precise recovery, and it is tighter thanthe existing bound for small K. Then, we study the largest choice of p for the p -minimization problem to recover any K-sparse signal, andthe largest recoverable K for a fixed p. Numerical experiments demonstrate the improvement of the proposed bounds in therecovery conditions over the up-to-date counterparts.

Research Area(s)

  • Compressed Sensing, Non-Convex Sparse Recovery, Null Space Property, Restricted Isometry Property, ℓp Pseudo Norm

Citation Format(s)

Sparse Recovery Conditions and Performance Bounds for -Minimization. / Yang, Chengzhu; Shen, Xinyue; Ma, Hongbing; Gu, Yuantao; So, Hing Cheung.

In: IEEE Transactions on Signal Processing, Vol. 66, No. 19, 01.10.2018, p. 5014-5028.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal