The problem of limited-angle computed tomography (CT) imaging reconstruction has a wide range of practical applications. Due to various factors such as high x-ray absorption, structural characteristics of the scanned object, and equipment limitations, it is often impractical to obtain a complete angular scan, resulting in limited-angle scan data. In this paper, we propose an iterative image reconstruction algorithm for limited-angle CT. The algorithm carries out a traditional CT reconstruction and a nonlinear diffusion process alternatively. Specifically, a subtle partial differential equation is constructed to guide the nonlinear diffusion process to eliminate limited-angle artifacts in the reconstructed image. Numerical experiments on both analytic data and real data validate the efficacy of the proposed nonlinear diffusion reconstruction algorithm. Furthermore, a linear diffusion reconstruction algorithm which combines a traditional CT reconstruction algorithm and a linear diffusion process is also presented in the paper.

中文翻译：

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基于非线性扩散模型的有限角度计算机断层扫描图像重建

有限角度计算机断层扫描（CT）成像重建问题具有广泛的实际应用。由于高X射线吸收、扫描物体的结构特征以及设备限制等多种因素，获得完整的角度扫描往往是不切实际的，从而导致扫描数据的角度有限。在本文中，我们提出了一种用于有限角度CT的迭代图像重建算法。该算法交替进行传统的CT重建和非线性扩散过程。具体来说，构建一个微妙的偏微分方程来指导非线性扩散过程，以消除重建图像中的有限角度伪影。解析数据和实际数据的数值实验验证了所提出的非线性扩散重建算法的有效性。此外，本文还提出了一种结合传统CT重建算法和线性扩散过程的线性扩散重建算法。