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

Date: Fri, October 31, 2014
Time: 12:30:00 - 00:00:00
Place: EOW 430

ABSTRACT

ABSTRACT:

Recent research has shown that compressible signals can be recovered from a very limited number of measurements by minimizing nonconvex functions that closely resemble the L0-norm function. These functions have sparse minimizers and, therefore, are called sparsity-promoting functions (SPFs). Recovery is achieved by solving a nonconvex optimization problem when using these SPFs. Contemporary methods for the solution of such difficult problems are inefficient and not supported by robust convergence theorems. In this seminar, sequential convex formulation methods for compressive sensing that can be used to solve nonconvex problems efficiently are proposed. Sparsity is promoted with a fairly general class of nonconvex SPFs that include widely used SPFs as special cases. Quadratic and piecewise-linear approximations of the SPF are employed and recovery is achieved by solving a sequence of convex optimization problems efficiently with state-of-the-art solvers. Convex problems are formulated as regularized least-squares, second-order cone programming, and weighted L1-norm minimization problems. The sequence of solution points is shown to be a monotonically decreasing sequence of values of the objective function and, consequently, converges to a sparse minimizer. Simulation results demonstrate that improved reconstruction performance, measurement consistency, and comparable computational cost are achieved with the proposed methods relative to competing state-of-the-art methods.