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Presenter: Flavio Teixeira
Supervisor: Drs. Stuart Bergen and Andreas Antoniou

Date: Fri, November 7, 2014
Time: 12:30:00 - 00:00:00
Place: EOW 430

ABSTRACT

ABSTRACT:

State-of-the-art methods applicable to the solution of nonconvex optimization problems in compressive sensing, such as convex formulation methods, are based on an indirect solution approach where approximation is employed. Unfortunately, indirect methods are inefficient for the solution of very-large-scale problems, typically in the range of a million variables, as they entail the solution of several subproblems of the same scale in sequence. In this seminar, proximal-point (PP) based methods that solve very-large-scale nonconvex optimization problems are proposed. Sparse-signal recovery is carried out by minimizing the sum of a nonconvex sparsity-promoting function (SPF) and the indicator function of a convex set. The objective function obtained in this way exhibits unusually rich properties from an optimization perspective. Recovery is achieved by iteratively performing two fundamental operations, namely, computation of the PP of the SPF and projection of the PP onto a convex set. The first operation is performed analytically or numerically by using a fast iterative method. The second operation is performed efficiently by computing a sequence of closed-form projectors. The sequence of points associated with the iterative computation is shown to converge to a minimizer and a two-step method with optimal convergence rate is employed for accelerated convergence. Simulation results demonstrate that improved reconstruction performance, measurement consistency, and comparable computational cost are achieved with the proposed methods relative to leading state-of-the-art competing methods. The proposed methods are robust, are supported by known convergence theorems, and lead to fast convergence. They are, as a consequence, particularly suitable for the solution of hard recovery problems of very-large size that entail large dynamic range and, are, in effect, strong candidates for use in many real-world applications.