AUTHOR=Zhou Zhiyong , Yu Jun 

TITLE=A New Nonconvex Sparse Recovery Method for Compressive Sensing

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 5 - 2019

YEAR=2019

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2019.00014

DOI=10.3389/fams.2019.00014

ISSN=2297-4687

ABSTRACT= As an extension of the widely used $\ell_r$-minimization with $0<r\leq 1$, a new non-convex weighted $\ell_r-\ell_1$ minimization method is proposed for compressive sensing. The theoretical recovery results based on restricted isometry property and $q$-ratio constrained minimal singular values are established. An algorithm that integrates the iteratively reweighted least squares algorithm and the difference of convex functions algorithm is given to approximately solve this non-convex problem. Numerical experiments are presented to illustrate our results.