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Information Center for Mathematical Science

PAC

A differential equations approach to l1-minimization with applications to array imaging
Author Lenya Ryzhik (Stanford University)
Homepage Url http://math.stanford.edu/~ryzhik/
Coauthors Miguel Moscoso, Alexei Novikov, George Papanicolaou
Abstract We present an ordinary differential equations approach to the analysis of algorithms for constructing l1 minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is independent of the relaxation parameter. An advantage of using the ordinary differential equations is that energy methods can be used to prove convergence. The connection to the discrete algorithms is provided by the Crandall-Liggett theory of monotone nonlinear semigroups. We illustrate the effectiveness of the discrete optimization algorithm in some sparse array imaging problems.
Abstract Url http://math.stanford.edu/~ryzhik/gelma-submit.pdf