Relaxed Averaged Alternating Reflections for Diffraction Imaging

Details Relaxed Averaged Alternating Reflections for Diffraction Imaging Relaxed Averaged Alternating Reflections for Diffraction Imaging

2004-05-12

arxiv.org/abs/math/0405208v1

Inverse Problems 21:37-50(2005)

Mathematics

Optimization and Control

13 pages, 19 figures

Scientific paper

10.1088/0266-5611/21/1/004

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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