Sparse recovery with coherent frames via ℓ1−2-analysis

This paper introduces a nonconvex Formula: see text-analysis model: Formula: see text where Formula: see text is a measurement matrix and Formula: see text is a tight frame. Our main motivation is to generalize the sparse recovery via Formula: see text minimization to this new model. As a nonconvex model, it is well known that its global minimizer and local minimizer are usually inconsistent. This paper provides a type of null space property (NSP) characterization which are necessary and sufficient conditions for the measurement matrix Formula: see text such that a vector Formula: see text can be recovered from Formula: see text with a tight frame Formula: see text via Formula: see text-analysis local minimization, or any vector Formula: see text can be uniformly recovered from Formula: see text with a tight frame Formula: see text via Formula: see text-analysis minimization locally and globally.