On an Extension of a Spare Regularization Model

Abstract

In this paper, we would first like to promote an interesting idea for identifying the local minimizer of a non-convex optimization problem with the global minimizer of a convex optimization one. Secondly, to give an extension of their sparse regularization model for inverting incomplete Fourier transforms introduced. Thirdly, following the same lines, to develop convergence guaranteed efficient iteration algorithm for solving the resulting nonsmooth and nonconvex optimization problem but here using applied nonlinear analysis tools. These both lead to a simplification of the proofs and to make a connection with classical works in this filed through a startling comment.