Zhang Yi, Zhang Weihua, Lei Yinjie, Zhou Jiliu
J Opt Soc Am A Opt Image Sci Vis. 2014 May 1;31(5):981-95. doi: 10.1364/JOSAA.31.000981.
This work presents a novel computed tomography (CT) reconstruction method for the few-view problem based on fractional calculus. To overcome the disadvantages of the total variation minimization method, we propose a fractional-order total variation-based image reconstruction method in this paper. The presented model adopts fractional-order total variation instead of traditional total variation. Different from traditional total variation, fractional-order total variation is derived by considering more neighboring image voxels such that the corresponding weights can be adaptively determined by the model, thus suppressing the over-smoothing effect. The discretization scheme of the fractional-order model is also given. Numerical and clinical experiments demonstrate that our method achieves better performance than existing reconstruction methods, including filtered back projection (FBP), the total variation-based projections onto convex sets method (TV-POCS), and soft-threshold filtering (STH).
这项工作提出了一种基于分数阶微积分的针对少视图问题的新型计算机断层扫描（CT）重建方法。为克服总变分最小化方法的缺点，本文提出了一种基于分数阶总变分的图像重建方法。所提出的模型采用分数阶总变分而非传统总变分。与传统总变分不同，分数阶总变分是通过考虑更多相邻图像体素推导得出的，这样相应的权重可由模型自适应确定，从而抑制过平滑效应。还给出了分数阶模型的离散化方案。数值实验和临床实验表明，我们的方法比现有的重建方法具有更好的性能，这些现有方法包括滤波反投影（FBP）、基于总变分的凸集投影方法（TV - POCS）和软阈值滤波（STH）。
