Recovery of sparsest signals via ${\ell }^q$-minimization

Abstract

In this paper, it is proved that every $s$-sparse vector $\mathbf{x}\in {\mathbb{R}}^n$ can be exactly recovered from the measurement vector $\mathbf{z}=\mathbf{A}\mathbf{x}\in {\mathbb{R}}^m$ via some ${\ell }^q$-minimization with $0<q\le 1$, as soon as each $s$-sparse vector $\mathbf{x}\in {\mathbb{R}}^n$ is uniquely determined by the measurement $\mathbf{z}$.

Cited by in corpus (1)

• Sparse approximation property and stable recovery of sparse signals from noisy measurements