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Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) are crucialtechnologies in the field of medical imaging. Score-based models have proven tobe effective in addressing different inverse problems encountered in CT andMRI, such as sparse-view CT and fast MRI reconstruction. However, these modelsface challenges in achieving accurate three dimensional (3D) volumetricreconstruction. The existing score-based models primarily focus onreconstructing two dimensional (2D) data distribution, leading toinconsistencies between adjacent slices in the reconstructed 3D volumetricimages. To overcome this limitation, we propose a novel two-and-a-half orderscore-based model (TOSM). During the training phase, our TOSM learns datadistributions in 2D space, which reduces the complexity of training compared todirectly working on 3D volumes. However, in the reconstruction phase, the TOSMupdates the data distribution in 3D space, utilizing complementary scores alongthree directions (sagittal, coronal, and transaxial) to achieve a more precisereconstruction. The development of TOSM is built on robust theoreticalprinciples, ensuring its reliability and efficacy. Through extensiveexperimentation on large-scale sparse-view CT and fast MRI datasets, our methoddemonstrates remarkable advancements and attains state-of-the-art results insolving 3D ill-posed inverse problems. Notably, the proposed TOSM effectivelyaddresses the inter-slice inconsistency issue, resulting in high-quality 3Dvolumetric reconstruction.

Two-and-a-half Order Score-based Model for Solving 3D Ill-posed Inverse Problems