EPFL | Biomedical Imaging Group | Proximity Operators

Proximity Operators for Phase Retrieval

F. Soulez, É. Thiébaut, A. Schutz, A. Ferrari, F. Courbin, M. Unser

Applied Optics, vol. 55, no. 26, pp. 7412–7421, September 10, 2016.

We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval. These proximity operators for noisy intensity measurements can replace the classical "noise-free" projection in any projection-based algorithm. They are derived from a maximum-likelihood formulation and admit closed form solutions for both the Gaussian and the Poisson cases. In addition, we extend these proximity operators to under-sampled intensity measurements. To assess their performance, these operators are exploited in a classical Gerchberg-Saxton algorithm. We present numerical experiments showing that the reconstructed complex amplitudes with these proximity operators always perform better than using the classical intensity projector, while their computational overhead is moderate.

@ARTICLE(http://bigwww.epfl.ch/publications/soulez1604.html,
AUTHOR="Soulez, F. and Thi{\'{e}}baut, {\'{E}}. and Schutz, A. and
	Ferrari, A. and Courbin, F. and Unser, M.",
TITLE="Proximity Operators for Phase Retrieval",
JOURNAL="Applied Optics",
YEAR="2016",
volume="55",
number="26",
pages="7412--7421",
month="September 10,",
note="")

© 2016 OSA. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from OSA. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.