有限数据CT重建 via 紧密框架与sinogram外推
Limited Tomography Reconstruction via Tight Frame and Sinogram Extrapolation
AI总结：
本文提出利用紧密框架正则化和同时sinogram外推方法，从有限sinogram数据中重建完整CT图像，优于传统稀疏模型方法。
摘要：
X射线计算机断层扫描（CT）是医疗和牙科人体断层成像中广泛使用的诊断工具之一。然而，标准的滤波反投影重建方法需要完整的投影数据知识。在有限数据的情况下，CT的逆问题变得更加病态，这使重建的图像受到伪影的破坏。本文考虑使用水平截断投影进行二维CT重建。几十年来，包括基于稀疏模型的方法在内的众多结果已经使从有限数据知识中重建感兴趣区域（ROI）内的图像成为可能。然而，与这些现有方法不同，我们尝试通过紧框架正则化和同时sinogram外推从有限的sinogram知识中重建整个CT图像。我们提出的方法在数值模拟结果上比现有的基于稀疏模型的方法更具前景。
英文摘要：
X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered backprojection reconstruction method requires the complete knowledge of the projection data. In the case of limited data, the inverse problem of CT becomes more ill-posed, which makes the reconstructed image deteriorated by the artifacts. In this paper, we consider two dimensional CT reconstruction using the horizontally truncated projections. Over the decades, the numerous results including the sparsity model based approach has enabled the reconstruction of the image inside the region of interest (ROI) from the limited knowledge of the data. However, unlike these existing methods, we try to reconstruct the entire CT image from the limited knowledge of the sinogram via the tight frame regularization and the simultaneous sinogram extrapolation. Our proposed model shows more promising numerical simulation results compared with the existing sparsity model based approach.
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