A new iterative firm-thresholding algorithm for inverse problems with sparsity constraints

In this paper we propose a variation of the soft-thresholding algorithm for finding sparse approximate solutions of the equation Ax=bAx=b, where as the sparsity of the iterate increases the penalty function changes. In this approach, sufficiently large entries in a sparse iterate are left untouched. The advantage of this approach is that a higher regularization constant can be used, leading to a significant reduction of the total number of iterations. Numerical experiments for sparse recovery problems, also with noisy data, are included.