Deep plug-and-play HIO approach for phase retrieval

In the phase retrieval problem, the aim is the recovery of an unknown image from intensity-only measurements such as Fourier intensity. Although there are several solution approaches, solving this problem is challenging due to its nonlinear and ill-posed nature. Recently, learning-based approaches have emerged as powerful alternatives to the analytical methods for several inverse problems. In the context of phase retrieval, a novel plug-and-play approach, to our knowledge, that exploits learning-based prior and efficient update steps has been presented at the Computational Optical Sensing and Imaging topical meeting, with demonstrated state-of-the-art performance. The key idea was to incorporate learning-based prior to the Gerchberg-Saxton type algorithms through plug-and-play regularization. In this paper, we present the mathematical development of the method including the derivation of its analytical update steps based on half-quadratic splitting and comparatively evaluate its performance through extensive simulations on a large test dataset. The results show the effectiveness of the method in terms of image quality, computational efficiency, and robustness to initialization and noise.