CT Reconstruction using Diffusion Posterior Sampling conditioned on a Nonlinear Measurement Model.

Area of Science:

• Medical Imaging
• Artificial Intelligence
• Computational Imaging

Background:

• Diffusion models are effective for image generation in CT reconstruction and restoration.
• Current diffusion posterior sampling methods for CT reconstruction rely on a linearized, approximate forward model.
• The inherent nonlinearity of X-ray CT physics is not fully captured by linear models.

Purpose of the Study:

• To develop a novel method for nonlinear CT image reconstruction using diffusion posterior sampling.
• To address the limitations of existing methods that approximate CT physics with linear models.
• To enable plug-and-play integration of diffusion priors with arbitrary nonlinear CT forward models.

Main Methods:

• Trained an unconditional diffusion model to estimate a prior score function.
• Derived a measurement likelihood score function from the nonlinear physical model of X-ray CT.
• Combined the prior and likelihood scores using Bayes' rule to obtain a posterior score function for sampling.

Main Results:

• Successfully reconstructed nonlinear CT images using diffusion posterior sampling.
• Demonstrated the method's effectiveness in low-dose and sparse-view CT geometries.
• Showcased the plug-and-play nature, allowing integration with different nonlinear CT systems without retraining.

Conclusions:

• The proposed method accurately reconstructs CT images from nonlinear forward models.
• Diffusion posterior sampling offers a powerful, flexible approach for advanced CT image reconstruction.
• The technique facilitates high-quality CT imaging in challenging acquisition scenarios.