Block-sparse Signal Reconstruction Using Alternating Direction Method

Block-sparse signal is a sparse signal with block structure. In practice, block-sparse signals arise in various applications, e.g., multi-band signals, DNA mi-croarrays, measuring gene expression levels, radar pulse signals, equalization ofsparse communication channels, magnetoencephalography, etc. Thus, the researchon block-sparse signal reconstruction algorithms has practical significance.In the article, we extend the alternating direction method technique （ADM）for l₁-minimization to the mixed l₂/l₁-norm optimization model for block-sparsesignal reconstruction. The ADM is applied to the unconstrained basis pursuit de-noising model and the basis pursuit model （BP） of block-sparse signal reconstruc-tion. In the BP model, we introduce the conjugate gradient method to solve thex-subproblem, and get better numerical results. Therefore, the application of AD-M in block-sparse signal reconstruction is feasible and stable.