Abstract:

The l_2,1-norm regularization can efficiently recover group-sparse signals whose non-zero coefficients occur in a few groups. It is well known that the l_2,1-norm regularization based on the classic alternating direction method shows strong stability and robustness in many applications. However, the l_2,1-norm regularization
requires more measurements. In order to recover groupsparse signals with a better sparsity-measurement tradeoff, the truncated l_2,1-norm regularization and reweighted l_2,1-norm regularization are proposed for the recovery of group-sparse signals based on the iterative support detection. The proposed algorithms are tested and compared with the l_2,1-norm model on a seriesof synthetic signals and the Shepp-Logan phantom. Experimental results demonstrate the performance of the proposed algorithms, especially at a low sample rate and high sparsity level.