Blind Ptychographic Phase Retrieval via Convergent Alternating Direction Method of Multipliers

TL;DR

This paper introduces a convergent alternating direction method of multipliers for blind ptychographic phase retrieval, improving reconstruction speed and quality by addressing a nonlinear least squares model with constraints and incorporating probe measurement information.

Contribution

It proposes a novel ADMM-based algorithm with convergence guarantees for nonconvex blind ptychography, outperforming existing methods in speed and image quality.

Findings

Algorithm converges under mild conditions

Outperforms state-of-the-art in speed

Produces higher quality reconstructions

Abstract

Ptychography has risen as a reference X-ray imaging technique: it achieves resolutions of one billionth of a meter, macroscopic field of view, or the capability to retrieve chemical or magnetic contrast, among other features. A ptychographyic reconstruction is normally formulated as a blind phase retrieval problem, where both the image (sample) and the probe (illumination) have to be recovered from phaseless measured data. In this article we address a nonlinear least squares model for the blind ptychography problem with constraints on the image and the probe by maximum likelihood estimation of the Poisson noise model. We formulate a variant model that incorporates the information of phaseless measurements of the probe to eliminate possible artifacts. Next, we propose a generalized alternating direction method of multipliers designed for the proposed nonconvex models with convergence guarantee under mild conditions, where their subproblems can be solved by fast element-wise operations. Numerically, the proposed algorithm outperforms state-of-the-art algorithms in both speed and image quality.