Phase retrieval via non-rigid image registration

TL;DR

This paper introduces a novel phase retrieval method using non-rigid image registration based on LDDMM, employing exterior calculus to handle various deformations, and evaluates its performance under different conditions.

Contribution

It presents a new phase retrieval approach leveraging non-rigid registration and exterior calculus, expanding the toolkit for coherent diffractive imaging.

Findings

Method effectively reconstructs images from diffraction data.

Performance varies with noise levels and image topology.

Numerical examples demonstrate robustness and flexibility.

Abstract

Phase retrieval is the numerical procedure of recovering a complex-valued signal from knowledge about its amplitude and some additional information. Here, an indirect registration procedure, based on the large deformation diffeomorphic metric mapping (LDDMM) formalism, is investigated as a phase retrieval method for coherent diffractive imaging. The method attempts to find a deformation which transforms an initial, template image to match an unknown target image by comparing the diffraction pattern to the data. The exterior calculus framework is used to treat different types of deformations in a unified and coordinate-free way. The algorithm performance with respect to measurement noise, image topology, and particular action are explored through numerical examples.