DDRM-PR: Fourier phase retrieval using denoising diffusion restoration models.

Area of Science:

• Computational imaging
• Image reconstruction
• Applied mathematics

Background:

• Diffusion models are effective learned priors for inverse problems.
• Current methods primarily address linear inverse problems.
• Nonlinear phase retrieval requires reconstructing images from intensity measurements.

Purpose of the Study:

• To adapt denoising diffusion restoration models (DDRMs) for nonlinear phase retrieval.
• To combine model-based methods with diffusion priors for improved image reconstruction.
• To address limitations of existing approaches in nonlinear phase retrieval.

Main Methods:

• Exploiting the posterior sampling framework of DDRMs.
• Integrating alternating-projection methods with pretrained unconditional diffusion priors.
• Applying the combined approach to Fourier intensity measurements.

Main Results:

• Demonstrated performance through simulations and experimental data.
• Showcased the potential of DDRMs for nonlinear phase retrieval.
• Identified both improvements and limitations of the proposed method.

Conclusions:

• DDRMs offer a promising direction for advancing nonlinear phase retrieval.
• The hybrid approach enhances model-based reconstruction techniques.
• Further research is needed to fully leverage diffusion models in this domain.