Deeply unrolled alternating projections for phase retrieval

Jiayi Yao, Vasileios Charisopoulos, Rebecca Willett

Deep unrolling methods for inverse problems augment traditional reconstruction algorithms with learned priors to improve their performance. These methods have been developed under the implicit assumption that the geometry of the measurement operator does not change between training and deployment; when this is no longer the case, the quality of obtained reconstructions can degrade significantly. In this paper, we argue that this is not an inherent limitation of the deep unrolling paradigm and can be mitigated by a careful choice of the underlying iterative algorithm. We propose a deep unrolling framework for the phase retrieval problem that augments the alternating projections method with a learned denoising step. Our method obtains high-quality reconstructions without the need for retraining in settings where conventional model-based alternatives struggle, such as when the dynamic range of the measurement operator changes significantly at test time.