A differential equations approach to l(1)-minimization with applications to array imaging Articles uri icon

publication date

  • October 2012


  • 10 (105001)


  • 28

International Standard Serial Number (ISSN)

  • 0266-5611

Electronic International Standard Serial Number (EISSN)

  • 1361-6420


  • We present an ordinary differential equation approach to the analysis of algorithms for constructing l(1) 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.