A Proximal Algorithm for Total Variation-Based Phase Retrieval

In this paper, I study the problem of phase retrieval with total variation (TV) smoothing and denoising. I construct an optimization model with an anisotropic TV penalty term, then show how to solve it using a proximal gradient method. This iterative-shrinkage-thresholding phase retrieval algorithm (ISTPRA) combines fixed-point iterations with a fast gradient solver for the convex subproblem. I compare my algorithm’s performance to several alternating projection methods. My results show that ISTPRA achieves a lower reconstruction error, while remaining robust to noise.