基于组稀疏正则化的少视图CT重建
Few-View CT Reconstruction with Group-Sparsity Regularization
摘要：
经典的基于全变分（TV）的迭代重建算法假设信号是分段光滑的，这导致重建结果受到过平滑效应的影响。为了解决这个问题，这项工作提出了一种新的计算机断层成像（CT）重建方法的少视图的问题称为组稀疏正则化为基础的同时代数重建技术（GSR-SART）。基于组的稀疏表示，它利用组的概念作为稀疏表示的基本单元，而不是一个补丁，被引入作为图像域的先验正则化项，以消除过度平滑的影响。通过将非局部斑块分组到不同的聚类中，用欧氏距离度量相似性，同时探索单个图像中的稀疏性和非局部相似性。采用分裂Bregman迭代算法得到数值格式。实验结果表明，我们的方法在定性和定量上都优于现有的几种重建方法，包括滤波反投影，期望最大化，SART，和基于TV的凸集投影。
英文摘要：
Classical total variation (TV) based iterative reconstruction algorithms assume that the signal is piecewise smooth, which causes reconstruction results to suffer from the over-smoothing effect. To address this problem, this work presents a novel computed tomography (CT) reconstruction method for the few-view problem called the group-sparsity regularization-based simultaneous algebraic reconstruction technique (GSR-SART). Group-based sparse representation, which utilizes the concept of a group as the basic unit of sparse representation instead of a patch, is introduced as the image domain prior regularization term to eliminate the over-smoothing effect. By grouping the nonlocal patches into different clusters with similarity measured by Euclidean distance, the sparsity and nonlocal similarity in a single image are simultaneously explored. The split Bregman iteration algorithm is applied to obtain the numerical scheme. Experimental results demonstrate that our method both qualitatively and quantitatively outperforms several existing reconstruction methods, including filtered back projection, expectation maximization, SART, and TV-based projections onto convex sets.
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