The essential ability of sparse reconstruction of different compressive sensing strategies

Abstract

We show the essential ability of sparse signal reconstruction of different compressive sensing strategies, which include the L1 regularization, the L0 regularization(thresholding iteration algorithm and OMP algorithm), the Lq(0 < q ⩽ 1) regularizations, the Log regularization and the SCAD regularization. Taking phase diagram as the basic tool for analysis, we find that (i) the solutions of the L0 regularization using hard thresh-olding algorithm and OMP algorithm are similar to those of the L1 regularization; (ii) the Lq regularization with the decreasing value of q, the Log regularization and the SCAD regularization can attain sparser solutions than the L1 regularization; (iii) the L1/2 regularization can be taken as a representative of the Lq(0 < q < 1) regularizations. When 1/2 < q < 1, the L1/2 regularization always yields the sparsest solutions and when 0 < q < 1/2 the performance of the regularizations takes no significant difference. The results of this paper provide experimental evidence for our previous work.