Sparse Signal Recovery With Minimization of 1-Norm Minus 2-Norm

Abstract

The key aim of compressed sensing is to stably recover a K-sparse signals x from a linear model y = Ax + v, where v is a noise vector. Minimization of ∥x∥ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -∥x∥ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> is a recently proposed effective recovery method. In this paper, we show that if the mutual coherence μ of A satisfies μ <; 1/3K, then this method can stably recover any K-sparse signal x based on y and A. As far as we know, this is the first sufficient condition based on mutual coherence for such method.