Fourier ptychographic microscopy using a generalized Anscombe transform approximation of the mixed Poisson-Gaussian likelihood.

Fourier ptychographic microscopy (FPM) is a novel computational microscopy technique that provides intensity images with both wide field-of-view (FOV) and high-resolution (HR). By combining ideas from synthetic aperture and phase retrieval, FPM iteratively stitches together a number of variably illuminated, low-resolution (LR) intensity images in Fourier space to reconstruct an HR complex sample image. In practice, however, the reconstruction of FPM is sensitive to the input noise, including Gaussian noise, Poisson shot noise or mixed Poisson-Gaussian noise. To efficiently address these noises, we developed a novel FPM reconstruction method termed generalized Anscombe transform approximation Fourier ptychographic (GATFP) reconstruction. The method utilizes the generalized Anscombe transform (GAT) approximation for the noise model, and a maximum likelihood theory is employed for formulating the FPM optimization problem. We validated the proposed method with both simulated data for quantitative evaluation and real experimental data captured using FPM setup. The results show that the proposed method achieves state-of-the-art performance in comparison with other approaches.