Non-convex block-sparse compressed sensing with coherent tight frames

Abstract

Abstract In this paper, we present a non-convex ℓ 2/ℓ q (0<q<1)-analysis method to recover a general signal that can be expressed as a block-sparse coefficient vector in a coherent tight frame, and a sufficient condition is simultaneously established to guarantee the validity of the proposed method. In addition, we also derive an efficient iterative re-weighted least square (IRLS) algorithm to solve the induced non-convex optimization problem. The proposed IRLS algorithm is tested and compared with the ℓ 2/ℓ 1-analysis and the ℓ q (0<q≤1)-analysis methods in some experiments. All the comparisons demonstrate the superior performance of the ℓ 2/ℓ q -analysis method with 0<q<1.

Keywords

• Block-sparse compressed sensing
• Restricted isometry property
• Restricted orthogonality property
• Tight frames
• ℓ 2/ℓ q -analysis method