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L1 optimization for robust signal processing

Shi, M. and Lukas, M.A. (2005) L1 optimization for robust signal processing. In: 18th National Conference of the Australian Society for Operations Research (ASOR) & 11th Australian Optimisation Day, 26 - 28 September, Perth, Western Australia.


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.

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