Efficient recovery of group-sparse signals with truncated and reweighted l2,1-regularization

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 group-sparse 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 series of 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.