On the conditional equivalence of phase retrieval algorithms

• URL: http://arxiv.org/abs/2606.07257v1
• Date: Fri, 05 Jun 2026 13:31:52 GMT
• Title: On the conditional equivalence of phase retrieval algorithms
• Abstract summary: We show that the GS magnitude replacement step is exactly a unit gradient descent step on an amplitude least-squares loss.<n>This equivalence enables seamless integration of classical phase retrieval with differentiable physics pipelines.
• Score: 0.34376560669160394
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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