CT reconstruction using diffusion posterior sampling conditioned on a nonlinear measurement model.

Area of Science:

• Medical Imaging
• Computational Imaging
• Artificial Intelligence in Medicine

Background:

• Diffusion posterior sampling (DPS) has shown promise in generating high-quality computed tomography (CT) images from low-quality data.
• Current DPS methods utilize a linear approximation of X-ray CT physics, which deviates from the inherently nonlinear forward model.
• This limitation restricts the adaptability and accuracy of existing DPS techniques in real-world CT applications.

Purpose of the Study:

• To develop and evaluate a novel diffusion posterior sampling (DPS) method that incorporates a general nonlinear measurement model for computed tomography (CT) image reconstruction.
• To address the limitations of current DPS approaches that rely on a linearized forward model, thereby improving reconstruction accuracy and flexibility.
• To demonstrate the capability of the proposed nonlinear DPS method to handle diverse CT systems and acquisition protocols without requiring retraining.

Main Methods:

• An unconditional diffusion model was implemented by training a prior score function estimator.
• Bayes' rule was applied to combine the diffusion prior with a measurement likelihood score function derived from the nonlinear physical model.
• The resulting posterior score function was used to sample the reverse-time diffusion process, with computational enhancements developed for efficiency.

Main Results:

• The proposed nonlinear DPS method demonstrated superior performance compared to traditional reconstruction techniques and DPS methods employing a linear model.
• Evaluations in simulation studies indicated that nonlinear DPS yields higher-quality CT images.
• The nonlinear DPS approach exhibited a better capacity for generating high-quality images across different acquisition protocols when compared to a conditionally trained deep learning approach.

Conclusions:

• The developed nonlinear DPS method offers a plug-and-play solution for integrating diffusion-based priors with general nonlinear CT measurement models.
• This approach enhances the applicability of DPS to various CT systems and protocols without the need for system-specific retraining.
• The findings highlight the potential of nonlinear DPS for advancing CT image reconstruction accuracy and adaptability.