L1 optimization for robust signal processing

Abstract

In this paper we develop special methods using the active set frameworkof the reduced gradient algorithm (RGA) to solve discrete L1 optimization problemswith a single linear equality constraint sT x = g, or a sequence of such problems withdifferent s = si and g = gi. These problems arise in certain large robust signal process-ing problems. The sequence of problems is solved recursively using ideas of sensitivityanalysis, by regarding the next problem as a perturbation of the previous problem. Thenumerical experiments illustrate that the proposed methods work very efficiently.