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.