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

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.

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.

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.

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.