Score-based generative model (SGM) has demonstrated great potential in the challenging limited-angle CT (LA-CT) reconstruction. SGM essentially models the probability density of the ground truth data and generates reconstruction results by sampling from it. Nevertheless, direct application of the existing SGM methods to LA-CT suffers multiple limitations. Firstly, the directional distribution of the artifacts attributing to the missing angles is ignored. Secondly, the different distribution properties of the artifacts in different frequency components have not been fully explored. These drawbacks would inevitably degrade the estimation of the probability density and the reconstruction results. After an in-depth analysis of these factors, this paper proposes a Wavelet-Inspired Score-based Model (WISM) for LA-CT reconstruction. Specifically, besides training a typical SGM with the original images, the proposed method additionally performs the wavelet transform and models the probability density in each wavelet component with an extra SGM. The wavelet components preserve the spatial correspondence with the original image while performing frequency decomposition, thereby keeping the directional property of the artifacts for further analysis. On the other hand, different wavelet components possess more specific contents of the original image in different frequency ranges, simplifying the probability density modeling by decomposing the overall density into component-wise ones. The resulting two SGMs in the image-domain and wavelet-domain are integrated into a unified sampling process under the guidance of the observation data, jointly generating high-quality and consistent LA-CT reconstructions. The experimental evaluation on various datasets consistently verifies the superior performance of the proposed method over the competing method.

中文翻译：

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用于有限角度 CT 重建的小波启发多通道评分模型


基于评分的生成模型 (SGM) 在具有挑战性的有限角度 CT (LA-CT) 重建中表现出了巨大的潜力。 SGM本质上是对地面真实数据的概率密度进行建模，并通过对其进行采样来生成重建结果。然而，将现有的 SGM 方法直接应用于 LA-CT 受到多种限制。首先，忽略了归因于缺失角度的伪影的方向分布。其次，不同频率分量中伪影的不同分布特性尚未得到充分探索。这些缺点将不可避免地降低概率密度的估计和重建结果。在对这些因素进行深入分析后，本文提出了一种用于 LA-CT 重建的小波启发评分模型（WISM）。具体来说，除了用原始图像训练典型的SGM之外，所提出的方法还执行小波变换并用额外的SGM对每个小波分量中的概率密度进行建模。小波分量在执行频率分解时保留了与原始图像的空间对应性，从而保留了伪影的方向特性以供进一步分析。另一方面，不同的小波分量在不同的频率范围内拥有原始图像的更具体的内容，通过将整体密度分解为分量密度来简化概率密度建模。由此产生的图像域和小波域中的两个 SGM 在观测数据的指导下集成到统一的采样过程中，共同生成高质量且一致的 LA-CT 重建。 对各种数据集的实验评估一致验证了所提出的方法相对于竞争方法的优越性能。