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

TL;DR

This paper introduces a novel two-and-a-half order score-based model (TOSM) that improves 3D volumetric reconstruction in medical imaging by addressing inter-slice inconsistency issues in CT and MRI.

Contribution

The paper proposes TOSM, a new score-based model that learns 2D data distributions during training and updates 3D distributions during reconstruction for better accuracy.

Findings

Achieves state-of-the-art results on sparse-view CT and fast MRI datasets.

Effectively addresses inter-slice inconsistency in 3D reconstructions.

Demonstrates robustness and reliability through theoretical foundations.

Abstract

Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) are crucial technologies in the field of medical imaging. Score-based models have proven to be effective in addressing different inverse problems encountered in CT and MRI, such as sparse-view CT and fast MRI reconstruction. However, these models face challenges in achieving accurate three dimensional (3D) volumetric reconstruction. The existing score-based models primarily focus on reconstructing two dimensional (2D) data distribution, leading to inconsistencies between adjacent slices in the reconstructed 3D volumetric images. To overcome this limitation, we propose a novel two-and-a-half order score-based model (TOSM). During the training phase, our TOSM learns data distributions in 2D space, which reduces the complexity of training compared to directly working on 3D volumes. However, in the reconstruction phase, the TOSM updates the data distribution in 3D space, utilizing complementary scores along three directions (sagittal, coronal, and transaxial) to achieve a more precise reconstruction. The development of TOSM is built on robust theoretical principles, ensuring its reliability and efficacy. Through extensive experimentation on large-scale sparse-view CT and fast MRI datasets, our method demonstrates remarkable advancements and attains state-of-the-art results in solving 3D ill-posed inverse problems. Notably, the proposed TOSM effectively addresses the inter-slice inconsistency issue, resulting in high-quality 3D volumetric reconstruction.