A very fast iterative algorithm for TV-regularized image reconstruction with applications to low-dose and few-view CT
A very fast iterative algorithm for TV-regularized image reconstruction with applications to low-dose and few-view CT
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DOI：
10.1117/12.2236788
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发表时间：
2016-09
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影响因子：
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通讯作者：
H. Kudo;F. Yamazaki;Takuya Nemoto;Keita Takaki
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文献类型：
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作者：
H. Kudo;F. Yamazaki;Takuya Nemoto;Keita Takaki
本文通过最小化用总变差（TV）惩罚正则化的数据保真度项，研究了低剂量少视点CT的迭代重建。我们提出了一个非常快速的迭代算法来解决这个问题。算法推导概述如下。首先，利用拉格朗日对偶性将原最小化问题转化为鞍点（原对偶）问题，并采用一阶原对偶迭代方法。其次，在不改变问题解的前提下，利用滤波后反投影（FBP）重构算法中的斜坡滤波器对迭代公式进行预处理。所得到的算法类似于所谓的迭代FBP算法的结构，并且快速收敛到代价函数的精确极小值。
This paper concerns iterative reconstruction for low-dose and few-view CT by minimizing a data-fidelity term regularized with the Total Variation (TV) penalty. We propose a very fast iterative algorithm to solve this problem. The algorithm derivation is outlined as follows. First, the original minimization problem is reformulated into the saddle point (primal-dual) problem by using the Lagrangian duality, to which we apply the first-order primal-dual iterative methods. Second, we precondition the iteration formula using the ramp filter of Filtered Backprojection (FBP) reconstruction algorithm in such a way that the problem solution is not altered. The resulting algorithm resembles the structure of so-called iterative FBP algorithm, and it converges to the exact minimizer of cost function very fast.