An Improved Sufficient Condition for Sparse Signal Recovery With Minimization of L1-L2

The l(1) - l(2)-minimization is widely used to stably recover a K-sparse signal x from its low dimensional measurements y = Ax + v, where A is a measurement matrix and v is a noise vector. In this paper, we show that if the mutual coherence mu of A satifies mu < 4K-1-root 8K+1/8 K-2-8 K then any K-sparse signal x can be stably recovered via the l(1) - l(2)-minimization. As far as we know, this is the best mutual coherence based sufficient condition of stably recovering K-sparse signals with the l(1) - l(2)-minimization.