Weakly Convex Regularized Robust Sparse Recovery Methods With Theoretical Guarantees

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

View graph of relations

Author(s)

  • Chengzhu Yang
  • Xinyue Shen
  • Hongbing Ma
  • Badong Chen
  • Yuantao Gu

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)5046-5061
Journal / PublicationIEEE Transactions on Signal Processing
Volume67
Issue number19
Online published19 Aug 2019
Publication statusPublished - 1 Oct 2019

Abstract

Robust sparse signal recovery against impulsive noise is a core issue in many applications. Numerous methods have been proposed to recover the sparse signal from measurements corrupted by various impulsive noises, but most of them either lack theoretical guarantee for robust sparse recovery or are not efficient enough for large-scale problems. To this end, a general optimization problem for robust sparse signal recovery, which includes many existing works as concrete instances, is analyzed by a freshly defined Double Null Space Property (DNSP), and its solution is proved to be able to robustly reconstruct the sparse signal under mild conditions. Moreover, for computational tractability, weakly convex sparsity-inducing penalties are applied to the general problem, and properties of the solution to the resultant non-convex problem are further studied. Based on these properties, an algorithm named Robust Projected Generalized Gradient (RPGG) is devised to solve the weakly convex problem. Theoretical results prove that the sparse signal can he precisely reconstructed by RPGG from compressive measurements with sparse noise or robustly recovered from those with impulsive noise. Meanwhile, simulations demonstrate that RPGG with tuned parameters outperforms other robust sparse recovery algorithms.

Research Area(s)

  • Compressed sensing, weakly convex, generalized gradient, robust sparse recovery, impulsive noise, REPRESENTATIONS, DICTIONARIES, CONSTANT

Citation Format(s)

Weakly Convex Regularized Robust Sparse Recovery Methods With Theoretical Guarantees. / Yang, Chengzhu; Shen, Xinyue; Ma, Hongbing; Chen, Badong; Gu, Yuantao; So, Hing Cheung.

In: IEEE Transactions on Signal Processing, Vol. 67, No. 19, 01.10.2019, p. 5046-5061.

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