SPARSE SIGNAL RECONSTRUCTION VIA THE APPROXIMATIONS OF l0 QUASINORM

In this paper, we propose two classes of the approximations to the cardinality function via the Moreau envelope of the l(1) norm. We show that these two approximations are good choices of the merit function for sparsity and are essentially the truncated l(1) norm and the truncated l(2) norm. Moreover, we apply the approximations to solve sparse signal recovery problems and then provide new weights for reweighted l(1) minimization and reweighted least squares to find sparse solutions of underdetermined linear systems of equations. Finally, we present some numerical experiments to illustrate our results.