A differential equations approach to l 1-minimization with applications to array imaging

Miguel Moscoso, Alexei Novikov, George Papanicolaou, Lenya Ryzhik

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number105001
JournalInverse Problems
Volume28
Issue number10
DOIs
StatePublished - Oct 2012

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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