基于二阶半阶评分模型求解三维不适定逆问题
Two-and-a-half Order Score-based Model for Solving 3D Ill-posed Inverse Problems
AI总结：
提出一种二阶半阶评分模型（TOSM），在训练时学习2D分布以降低复杂度，重建时在3D空间利用三方向互补评分，解决CT和MRI中3D不适定逆问题的切片间不一致，实现高质量重建。
摘要：
计算机断层扫描（CT）和磁共振成像（MRI）是医学成像领域的关键技术。基于评分的模型已被证明能有效解决CT和MRI中遇到的不同逆问题，如稀疏视角CT和快速MRI重建。然而，这些模型在实现精确的三维（3D）体积重建方面面临挑战。现有的基于评分的模型主要关注重建二维（2D）数据分布，导致重建的3D体积图像中相邻切片之间出现不一致。为克服这一局限，我们提出了一种新颖的二阶半阶评分模型（TOSM）。在训练阶段，我们的TOSM学习2D空间中的数据分布，与直接在3D体积上工作相比，降低了训练复杂度。然而，在重建阶段，TOSM在3D空间中更新数据分布，利用沿三个方向（矢状面、冠状面和横断面）的互补评分以实现更精确的重建。TOSM的开发建立在坚实的理论基础之上，确保其可靠性和有效性。通过在大型稀疏视角CT和快速MRI数据集上的广泛实验，我们的方法在解决3D不适定逆问题方面展现出显著进步并达到了最先进的结果。值得注意的是，所提出的TOSM有效解决了切片间不一致问题，实现了高质量的3D体积重建。
英文摘要：
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.
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