Plug-and-play optimization for pixel super-resolution phase retrieval

In order to increase signal-to-noise ratio in measurement, most imaging detectors sacrifice resolution to increase pixel size in confined area. Although the pixel super-resolution technique (PSR) enables resolution enhancement in such as digital holographic imaging, it suffers from unsatisfied reconstruction quality. In this work, we report a high-fidelity plug-and-play optimization method for PSR phase retrieval, termed as PNP-PSR. It decomposes PSR reconstruction into independent sub-problems based on the generalized alternating projection framework. An alternating projection operator and an enhancing neural network are derived to tackle the measurement fidelity and statistical prior regularization, respectively. In this way, PNP-PSR incorporates the advantages of individual operators, achieving both high efficiency and noise robustness. We compare PNP-PSR with the existing PSR phase retrieval algorithms with a series of simulations and experiments, and PNP-PSR outperforms the existing algorithms with as much as 11dB on PSNR. The enhanced imaging fidelity enables one-order-of-magnitude higher cell counting precision.