A sufficient condition for restoring sparse vectors from ℓ1−ℓ2$\ell _1-\ell _2$‐minimization with cumulative coherence.

This paper focuses on the compressed sensing ℓ1−ℓ2$\ell _1-\ell _2$‐minimization model and develops new bounds on cumulative coherence μ1(s)$\mu _1(s)$. It is pointed out that if cumulative coherence μ1(s)$\mu _1(s)$ satisfies Equation (2) or (11), then the sparse signal can stably recover in noise model and exactly recover in free noise by ℓ1−ℓ2$\ell _1-\ell _2$‐minimization model. From this paper, it is found that based on some condition of cumulative coherence, the ℓ1−ℓ2$\ell _1-\ell _2$‐minimization model can exactly recover s‐sparse signals in noiseless cases and stably recover s‐sparse signals in the noise cases. [ABSTRACT FROM AUTHOR]