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

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

2010-05-03

arxiv.org/abs/1005.0267v1

Computer Science

Information Theory

Scientific paper

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

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