Alternating Phase Langevin Sampling with Implicit Denoiser Priors for Phase Retrieval

• URL: http://arxiv.org/abs/2211.00884v2
• Date: Tue, 9 May 2023 23:21:40 GMT
• Title: Alternating Phase Langevin Sampling with Implicit Denoiser Priors for Phase Retrieval
• Authors: Rohun Agrawal, Oscar Leong
• Abstract summary: We present a way leveraging the prior implicitly learned by a denoiser to solve phase retrieval problems by incorporating it in a classical framework. Compared to performant denoising-based algorithms for phase retrieval, we showcase competitive performance with notable measurements on in-distribution images and notable out-of-distribution images.
• Score: 1.7767466724342065
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is highly ill-posed due to the phase-induced ambiguities and the large number of possible images that can fit to the given measurements. Thus, there's a rich history of enforcing structural priors to improve solutions including sparsity priors and deep-learning-based generative models. However, such priors are often limited in their representational capacity or generalizability to slightly different distributions. Recent advancements in using denoisers as regularizers for non-convex optimization algorithms have shown promising performance and generalization. We present a way of leveraging the prior implicitly learned by a denoiser to solve phase retrieval problems by incorporating it in a classical alternating minimization framework. Compared to performant denoising-based algorithms for phase retrieval, we showcase competitive performance with Fourier measurements on in-distribution images and notable improvement on out-of-distribution images.

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