Newton, Marcus (2012) Compressed sensing for phase retrieval. Physical Review E, 85 (5), 056706-1 - 056706-5. (doi:10.1103/PhysRevE.85.056706).
Abstract
To date there are several iterative techniques that enjoy moderate success when reconstructing phase information, where only intensity measurements are made. There remains, however, a number of cases in which conventional approaches are unsuccessful. In the last decade, the theory of compressed sensing has emerged and provides a route to solving convex optimisation problems exactly via l(1)-norm minimization. Here the application of compressed sensing to phase retrieval in a nonconvex setting is reported. An algorithm is presented that applies reweighted l(1)-norm minimization to yield accurate reconstruction where conventional methods fail.
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