DDRM-PR: Fourier Phase Retrieval using Denoising Diffusion Restoration Models
This work addresses phase retrieval, a problem in imaging and signal processing, by extending diffusion models to nonlinear inverse problems, though it appears incremental as it builds on existing DDRM and alternating-projection techniques.
The paper tackled the nonlinear phase retrieval problem of reconstructing images from noisy intensity-only measurements like Fourier intensity by combining alternating-projection methods with Denoising Diffusion Restoration Models (DDRM) to use pretrained diffusion priors. Results from simulations and experimental data showed potential improvements for alternating-projection methods but also highlighted limitations.
Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior sampling framework of Denoising Diffusion Restoration Models (DDRM) for the solution of nonlinear phase retrieval problem, which requires reconstructing an image from its noisy intensity-only measurements such as Fourier intensity. The approach combines the model-based alternating-projection methods with the DDRM to utilize pretrained unconditional diffusion priors for phase retrieval. The performance is demonstrated through both simulations and experimental data. Results demonstrate the potential of this approach for improving the alternating-projection methods as well as its limitations.