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

Shudong Li; Xiao Jiang; Matthew Tivnan; Grace J. Gang; Yuan Shen; J. Webster Stayman

doi:10.1117/1.JMI.11.4.043504

30 August 2024 CT reconstruction using diffusion posterior sampling conditioned on a nonlinear measurement model

Shudong Li, Xiao Jiang, Matthew Tivnan, Grace J. Gang, Yuan Shen, J. Webster Stayman

Author Affiliations +

Journal of Medical Imaging, Vol. 11, Issue 4, 043504 (August 2024). https://doi.org/10.1117/1.JMI.11.4.043504

Abstract

Purpose

Recently, diffusion posterior sampling (DPS), where score-based diffusion priors are combined with likelihood models, has been used to produce high-quality computed tomography (CT) images given low-quality measurements. This technique permits one-time, unsupervised training of a CT prior, which can then be incorporated with an arbitrary data model. However, current methods rely on a linear model of X-ray CT physics to reconstruct. Although it is common to linearize the transmission tomography reconstruction problem, this is an approximation to the true and inherently nonlinear forward model. We propose a DPS method that integrates a general nonlinear measurement model.

Approach

We implement a traditional unconditional diffusion model by training a prior score function estimator and apply Bayes’ rule to combine this prior with a measurement likelihood score function derived from the nonlinear physical model to arrive at a posterior score function that can be used to sample the reverse-time diffusion process. We develop computational enhancements for the approach and evaluate the reconstruction approach in several simulation studies.

Results

The proposed nonlinear DPS provides improved performance over traditional reconstruction methods and DPS with a linear model. Moreover, as compared with a conditionally trained deep learning approach, the nonlinear DPS approach shows a better ability to provide high-quality images for different acquisition protocols.

Conclusion

This plug-and-play method allows the incorporation of a diffusion-based prior with a general nonlinear CT measurement model. This permits the application of the approach to different systems, protocols, etc., without the need for any additional training.

Citation Download Citation

Shudong Li, Xiao Jiang, Matthew Tivnan, Grace J. Gang, Yuan Shen, and J. Webster Stayman "CT reconstruction using diffusion posterior sampling conditioned on a nonlinear measurement model," Journal of Medical Imaging 11(4), 043504 (30 August 2024). https://doi.org/10.1117/1.JMI.11.4.043504

Received: 22 December 2023; Accepted: 31 July 2024; Published: 30 August 2024

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