RED-PhaseCut: A Variational Sampler Using Diffusion Model for Fourier Phase Retrieval

Fourier phase retrieval is a representative inverse problem where a signal has to be recovered only using the measured magnitude of the Fourier transform of the signal. Deep learning-based algorithms offer more satisfactory reconstructions than standard algorithms, such as alternating projection approaches and convex relaxation methods. However, they often cannot reconstruct fine details or textures. Recently, diffusion models have been utilized to address the Fourier phase retrieval problems. These algorithms provide realistic results, but the non-existent details in the actual images can be shown in the reconstruction because of the nature of generative models. To cope with these problems, we proposed a novel algorithm, dubbed RED-PhaseCut, combining a variational diffusion sampling approach and the convex relaxation approach for phase retrieval. In particular, the classical optimization problem for phase retrieval is utilized as additional regularization for correctly reconstructing phase information during the variational sampling process. Our experimental results confirm that the proposed RED-PhaseCut provides qualitatively and quantitatively improved performance compared to the existing Fourier phase retrieval algorithms.