Uniqueness transition in noisy phase retrieval

TL;DR

This paper introduces a new information-theoretic criterion for phase retrieval feasibility in noisy conditions, applicable to fields like magnetic imaging, revealing a spin-glass-like transition in uniqueness.

Contribution

It proposes a Shannon mutual information-based criterion for phase retrieval, improving upon Maxwell's principle, especially under noise and strong priors.

Findings

Uniqueness transition resembles spin glass behavior.

Criterion depends on photons per pixel exceeding a threshold.

Applicable to magnetic domain imaging and similar fields.

Abstract

Previous criteria for the feasibility of reconstructing phase information from intensity measurements, both in x-ray crystallography and more recently in coherent x-ray imaging, have been based on the Maxwell constraint counting principle. We propose a new criterion, based on Shannon's mutual information, that is better suited for noisy data or contrast that has strong priors not well modeled by continuous variables. A natural application is magnetic domain imaging, where the criterion for uniqueness in the reconstruction takes the form that the number of photons, per pixel of contrast in the image, exceeds a certain minimum. Detailed studies of a simple model show that the uniqueness transition is of the type exhibited by spin glasses.