UPrime: Unrolled Phase Retrieval Iterative Method with provable convergence

Abstract

Phase Retrieval (PR) is an ill-posed inverse problem which arises in various science and engineering applications. Recently, it has been empirically shown that unrolled iterative methods or model-driven deep learning methods are effective for solving this problem. However, the prior modules in these model-driven networks lack model interpretability, leading to a lack of rigorous analysis about the convergence behaviors of these re-implemented iterations, and thus the significance of such PR methods is a little bit vague. For this issue, this paper proposes an effective and provable Unrolled Phase Retrieval Iterative MEthod (UPrime) for the PR problem. Our theoretical analysis demonstrates that UPrime using an elaborated bounded prior module can generate fixed-point convergent trajectories. Meanwhile, the proposed prior module, a flexible and interpretable module, is beneficial for the convergence analysis of regularized imaging methods in the non-convex scenario. Experiments on coded diffraction imaging applications verify the superiority of UPrime.