Stochastic Multigrid Method for Blind Ptychographic Phase Retrieval

TL;DR

This paper introduces eMAGPIE, a stochastic multigrid algorithm for blind ptychographic phase retrieval that efficiently recovers both object and probe, achieving faster convergence and improved reconstruction quality.

Contribution

The paper presents a novel stochastic multigrid method with closed-form updates for joint object and probe recovery in ptychography, enhancing convergence speed and reconstruction quality.

Findings

eMAGPIE achieves lower data misfit and phase error.

Produces smoother, artifact-reduced phase reconstructions.

Speeds up convergence through multigrid acceleration.

Abstract

We present eMAGPIE (extended Multilevel-Adaptive-Guided Ptychographic Iterative Engine), a stochastic multigrid method for blind ptychographic phase retrieval that jointly recovers the object and the probe. We recast the task as the iterative minimization of a quadratic surrogate that majorizes the exit-wave misfit. From this surrogate, we derive closed-form updates, combined in a geometric-mean, phase-aligned joint step, yielding a simultaneous update of the object and probe with guaranteed descent of the sampled surrogate. This formulation naturally admits a multigrid acceleration that speeds up convergence. In experiments, eMAGPIE attains lower data misfit and phase error at comparable compute budgets and produces smoother, artifact-reduced phase reconstructions.