Solving ptychography with a convex relaxation

TL;DR

This paper introduces a convex optimization approach to ptychography that guarantees stability and robustness, improves reconstruction accuracy, and outperforms traditional algorithms like alternating projections.

Contribution

It presents a novel convex formulation for ptychography that eliminates local minima and enables the use of efficient algorithms with theoretical guarantees.

Findings

Achieves 25% lower background variance than standard methods

Supports noise modeling and multiple a priori constraints

Runs with near-linear runtime and memory usage

Abstract

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the current standard algorithm for ptychographic reconstruction.