Stable Cosparse Recovery via \ell_p-analysis Optimization

Abstract

In this paper we study the ${\ell }_p$-analysis optimization ($0<p\le 1$) problem for cosparse signal recovery. We establish a bound for recovery error via the restricted $p$-isometry property over any subspace. We further prove that the nonconvex ${\ell }_q$-analysis optimization can do recovery with a lower sample complexity and in a wider range of cosparsity than its convex counterpart. In addition, we develop an iteratively reweighted method to solve the optimization problem under a variational framework. Empirical results of preliminary computational experiments illustrate that the nonconvex method outperforms its convex counterpart.