The essential ability of sparse reconstruction of different compressive sensing strategies

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 L_q(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 L_q regularization with the decreasing value of q, the Log regularization and the SCAD regularization can attain sparser solutions than the L₁ regularization; (iii) the L_1/2 regularization can be taken as a representative of the L_q(0 < q < 1) regularizations. When 1/2 < q < 1, the L_1/2 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.