Fourier Phase Retrieval With Diffusion Priors Guided by Failure Detection

Fourier phase retrieval (FPR) is a longstanding ill-posed non-convex inverse problem suffering from failure in reconstruction. Existing methods usually mitigate the issue in a trial-and-error fashion and cannot identify the failure to flexibly adjust the FPR process. In this paper, we propose FA-FPR, a novel failure aware method that guides FPR with diffusion priors by failure detection. We first discover that unsuccessful reconstructions can be identified as fake images due to their distinct structures from true signals, and then leverage a plug-and-play fake image detector to automatically determine the approximation to true signals. Furthermore, we develop a hybrid decoupling scheme that adaptively combines Gaussian noise and predicted noise by score function based on the failure detection. Extensive experiments under various oversampling ratios with noisy and noiseless measurements demonstrate that FA-FPR requires less than 50% number of repeated experiments on average to achieve the state-of-the-art performance.