Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient

TL;DR

This paper introduces a novel Fourier ptychographic reconstruction method that employs Poisson maximum likelihood and truncated Wirtinger gradient to improve image quality under noise and measurement errors.

Contribution

It presents a new FP reconstruction algorithm combining Poisson likelihood and truncated Wirtinger gradient, enhancing robustness against noise and errors.

Findings

Outperforms existing algorithms on simulated data

Effective noise and error mitigation demonstrated

Source code released for non-commercial use

Abstract

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample's high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for error removal. Results on both simulated data and real data captured using our laser FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use.