Large 00011

From Convex Feasibility to Optimization in Signal Recovery and Learning

Patrick Combettes

Recorded 10 July 2013 in Lausanne, Vaud, Switzerland

Event: Spars 2013 - Signal Processing with Adaptive Sparse Structured Representations

Abstract

A key issue in inverse problems and learning is to represent prior information in a ?exible, reliable, and numerically viable setting. The formulation of such problems as convex feasibility problems is deep rooted in the literature [1], [2], [4]. In recent years, increasingly complex optimization approaches have emerged to solve a variety of problems in these areas, e.g., [3], [5]. The objective of this talk is to compare the two approaches from the viewpoint of reliable information modeling and numerical algorithms. Using convex analytical tools, we shall also show how most current optimization models can be derived from feasibility formulations. In particular, sparsity information modeling will be discussed.

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