  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.
