Deep nonlocal low-rank regularization for complex-domain pixel super-resolution

Pixel super-resolution (PSR) has emerged as a promising technique to break the sampling limit for phase imaging systems. However, due to the inherent nonconvexity of phase retrieval problem and super-resolution process, PSR algorithms are sensitive to noise, leading to reconstruction quality inevitably deteriorating. Following the plug-and-play framework, we introduce the nonlocal low-rank (NLR) regularization for accurate and robust PSR, achieving a state-of-the-art performance. Inspired by the NLR prior, we further develop the complex-domain nonlo-cal low-rank network (CNLNet) regularization to perform nonlocal similarity matching and low-rank approximation in the deep feature domain rather than the spatial domain of conventional NLR. Through visual and quantitative comparisons, CNLNet-based reconstruction shows an average 1.4 dB PSNR improvement over conventional NLR, outperforming existing algorithms under various scenarios.