  Complex-domain imaging has emerged as a valuable technique for investigating
weak-scattered samples. However, due to the detector's pursuit of large pixel
size for high throughput, the resolution limitation impedes its further
development. In this work, we report a lensless on-chip complex-domain imaging
system, together with a distributed-optimization-based pixel super-resolution
technique (DO-PSR). The system employs a diffuser shifting to realize phase
modulation and increases observation diversity. The corresponding DO-PSR
technique derives an alternating projection operator and an enhancing neural
network to tackle the measurement fidelity and statistical prior regularization
subproblems. Extensive experiments show that the system outperforms the
existing techniques with as much as 11dB on PSNR, and one-order-of-magnitude
higher cell counting precision.
