Diffusion Posterior Sampling for Tomographic Reconstruction with Mixed Resolution Priors.

Deep learning has demonstrated an excellent capacity to capture prior information about image classes. This has driven advances in image formation to break through traditional limits of data fidelity in denoising, reconstruction, and processing of undersampled data. Diffusion posterior sampling (DPS) is one approach that combines a generative prior with an analytic model for the measurements to both enforce consistency with measurements and also integrate sophisticated prior information. In such approaches, performance gains can be limited by the quality of the deep learning prior, which, in turn, is limited by the data used to train that network model. In many cases, like tomographic reconstruction, training data is assembled from standard clinical protocols. Specialized, high-fidelity datasets (e.g. very high spatial resolution scans) are often limited in number and/or only target regional anatomy. We propose a novel DPS framework for image reconstruction that uses mixed prior models to enhance regional spatial resolution while maintaining global information for stability and consistency. Specifically, the method integrates a global diffusion model, trained on (untruncated) normal-resolution data, with a regional patch-based diffusion model, trained on high-resolution patches. The prior models are combined using frequency-domain methods, where low-frequency components are extracted from the global model and high-frequency components come from the patch-based model. To address boundary discontinuities inherent to patch-based diffusion model, we adopt a shifted patch division mechanism, which dynamically moves patch boundaries across sampling steps. This strategy removes the stitching artifacts by dispersing them as stochastic noise, while the diffusion prior and posterior constraints gradually eliminate residual inconsistencies. Furthermore, a resampling step is applied after each likelihood update, ensuring stability and preventing error accumulation across iterations. Finally, we introduce a regional sampling scheme, where a binary mask ensures the regional prior is applied within the appropriate anatomy, while the global prior is applied in the background. Experimental results demonstrate that the proposed framework achieves superior reconstruction quality by preserving fine-grained details in regions of interest without sacrificing global structural coherence. This work highlights the potential of combining multi-scale diffusion priors for high-fidelity and efficient posterior sampling in inverse imaging problems.