Compressed Sensing with coherent tight frames via $l_q$-minimization for $0<q\le 1$

Abstract

Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee accurate recovery of signals which are sparse in the tight frame, from undersampled data with minimal $l_1$-norm of transform coefficients. This improves the result in [1]. Also, the $l_q$-minimization $(0<q<1)$ approaches are introduced. We show that under a suitable condition, there exists a value $q_0\in (0,1]$ such that for any $q\in (0,q_0)$, each solution of the $l_q$-minimization is approximately well to the true signal. In particular, when the tight frame is an identity matrix or an orthonormal basis, all results obtained in this paper appeared in [13] and [26].

References in corpus (1)

• Compressed Sensing and Redundant Dictionaries

Cited by in corpus (1)

• Smoothing and Decomposition for Analysis Sparse Recovery