Fourier Diffusion Models: A Method to Control MTF and NPS in Score-Based Stochastic Image Generation.

Area of Science:

• Artificial Intelligence
• Medical Imaging
• Computational Science

Background:

• Score-based diffusion models are powerful for image generation but computationally intensive.
• Existing models require numerous neural network passes for sampling, limiting practical application.
• The forward process typically involves additive white noise and input scaling.

Purpose of the Study:

• To introduce Fourier Diffusion Models (FDMs) as a more efficient alternative for image generation.
• To enable posterior sampling of high-quality images from blurry, noisy measurements.
• To improve image quality in medical imaging applications using diffusion models.

Main Methods:

• Replaced scalar operations in the forward diffusion process with linear shift-invariant systems and spatially-stationary noise.
• Modeled continuous probability flow from true images to measurements defined by a specific modulation transfer function (MTF) and noise power spectrum (NPS).
• Derived the reverse process for posterior sampling.

Main Results:

• FDMs allow modeling of probability flow with specific system characteristics (MTF, NPS).
• Demonstrated improved image quality for supervised diffusion posterior sampling compared to existing conditional models.
• Successfully applied to simulated CT measurements with correlated noise and system blur using the LIDC dataset.

Conclusions:

• Fourier Diffusion Models offer a computationally efficient and effective approach to image generation and reconstruction.
• FDMs show significant potential for enhancing image quality in medical imaging and other fields.
• The proposed method addresses key limitations of traditional score-based diffusion models.