A new iterative weighted norm minimization algorithm and its applications

A general class of linear inverse problems in which the solutions are sparse and localized is considered. The proposed algorithm is a nonparametric approach that finds sparse and localized solutions without prior information on the constraints. Each step of the iterative procedure consists in solving a weighted least squares problem wherein the weighting matrix is determined by the solution from the previous iteration. Some properties of the algorithm along with its applications to problems in direction of arrival and spectrum estimation are presented.<>