Accelerated Wirtinger Flow for Multiplexed Fourier Ptychographic Microscopy

TL;DR

This paper introduces an accelerated, parameter-free gradient descent algorithm for multiplexed Fourier ptychographic microscopy, significantly improving convergence speed while maintaining high-quality high-resolution imaging from low-resolution, multiplexed measurements.

Contribution

It develops a novel, analytically derived step size for gradient descent in multiplexed Fourier ptychography, enabling faster, parameter-free reconstruction with proven convergence guarantees.

Findings

Accelerated algorithm converges faster than non-accelerated versions.

Parameter-free approach performs comparably to manually tuned methods.

Validated on real data demonstrating practical applicability.

Abstract

Fourier ptychographic microscopy enables gigapixel-scale imaging, with both large field-of-view and high resolution. Using a set of low-resolution images that are recorded under varying illumination angles, the goal is to computationally reconstruct high-resolution phase and amplitude images. To increase temporal resolution, one may use multiplexed measurements where the sample is illuminated simultaneously from a subset of the angles. In this paper, we develop an algorithm for Fourier ptychographic microscopy with such multiplexed illumination. Specifically, we consider gradient descent type updates and propose an analytical step size that ensures the convergence of the iterates to a stationary point. Furthermore, we propose an accelerated version of our algorithm (with the same step size) which significantly improves the convergence speed. We demonstrate that the practical performance of our algorithm is identical to the case where the step size is manually tuned. Finally, we apply our parameter-free approach to real data and validate its applicability.