Fourier ptychographic reconstruction based on an augmented Lagrangian method and sparse approximations for phase and magnitude

Fourier ptychography microscopy provides a large field of view and high-resolution imaging by simultaneously recovering intensity and phase distributions. However, in real setups, the process of capturing large numbers of low-resolution images will inevitably suffer from imaging noise, which could seriously distort the results recovered using the conventional Fourier ptychography approach. To suppress the effects of imaging noise optimally, a novel, to the best of our knowledge, iterative algorithm is proposed. This algorithm consists of two objective functions; one is based on the augmented Lagrangian function for the inverse computation, and its solution is found by utilizing the alternating direction multiplier method; the other is the separate sparse model built for amplitude and absolute phase image; the filtering process is accomplished by exploiting the block-matching 3D frames. In combination with the Nash equilibrium balancing theory, the proposed algorithm is realized by alternately optimizing the two objective functions. The simulated and experimental results demonstrate that the proposed algorithm is robust to noise and is capable of reconstructing complete and good contrast amplitude and phase images.