Sparse recovery with coherent frames via ℓ1−2-analysis.

This paper introduces a nonconvex ℓ1−2-analysis model: minx(∥D∗x∥ 1 −∥D∗x∥ 2)s.t. Ax = y, where A is a measurement matrix and D is a tight frame. Our main motivation is to generalize the sparse recovery via ℓ1 − ℓ2 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 A such that a vector x can be recovered from Ax with a tight frame D via ℓ1−2-analysis local minimization, or any vector x can be uniformly recovered from Ax with a tight frame D via ℓ1−2-analysis minimization locally and globally. [ABSTRACT FROM AUTHOR]