The essential ability of sparse reconstruction of different compressive sensing strategies - Liang Yong

We show the essential ability of sparse signal reconstruction of different compressive sensing strategies, which include the L 1 regularization, the L 0 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 L 0 regularization using hard thresh-olding algorithm and OMP algorithm are similar to those of the L 1 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 L 1 regularization; (iii) the L 1/2 regularization can be taken as a representative of the L q …