Relaxed Averaged Alternating Reflections for Diffraction Imaging

2004/05/12 by D. Russell Luke, D Russell Luke · 3 citations
Mathematics · Physics and Astronomy · #math-ph #math.MP #math.OC #msc:30E10 #msc:49M27 #msc:49M45 #msc:78M50 #physics.optics

paper · pdf · doi:10.1088/0266-5611/21/1/004

published as Inverse Problems 21:37-50(2005) · 13 pages, 19 figures

arxiv created 2004/05/12 · arxiv updated 2009/12/01

Abstract

We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged alternating reflectors and determine the fixed point set of the related operator in the convex case. A numerical study supports our theoretical observations and demonstrates the effectiveness of the algorithm compared to the current state of the art.

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