On the Conditional Equivalence of Phase Retrieval Algorithms

MCML Authors

Andreas Döpp

Dr. habil

Collaborating PI

Data-driven methods in Physics and Optics

Abstract

Phase retrieval - recovering a complex-valued field from intensity measurements - is typically solved using variants of the Gerchberg-Saxton (GS) algorithm, understood as alternating projections between measurement planes. Meanwhile, modern computational imaging increasingly relies on gradient-based optimization and automatic differentiation. Here we show that these two approaches are mathematically identical: the GS magnitude replacement step is exactly a unit gradient descent step on an amplitude least-squares loss. This equivalence enables seamless integration of classical phase retrieval with differentiable physics pipelines. We further identify two complementary probabilistic interpretations of this equivalence: globally, the amplitude loss is the negative log-likelihood under Gaussian amplitude noise; locally, each projection step arises as a Bayesian update with the propagated field as prior. The local view provides qualitative guidance for relaxation in iterative phase retrieval.

article SD26b

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Machine Learning: Science and Technology

7.037001. Jun. 2026.

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Authors

J. Schroeder • A. Döpp

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Links

DOI

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Research Area

 A1 | Statistical Foundations & Explainability