A weighted optimization for Fourier Ptychographic Microscopy

Abstract

Fourier ptychography can be implemented as a phase retrieval optimization algorithm that iteratively solves for high resolution spectrum from low resolution images. In prior art, all the low resolution images were considered equally in the optimization. In this paper, we propose a weighted optimization algorithm to enhance the quality of reconstruction with the same convergence speed. Our method is motivated by the observation that bright field and dark field low resolution images have significantly different pixel intensities. Therefore, we weight their estimated error differently in the optimization. Though the proposed method is both conceptually and computationally simple, it dramatically improves the quality of reconstruction. We also show that the weighted optimization algorithm converges to a lower mean squared error value compared to the conventional optimization. We validate our approach on several low resolution images from an experimental dataset.