Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction.
Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction.
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用于最大后验 ECT 重建的预处理交替投影算法
DOI：
10.1088/0266-5611/28/11/115005
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发表时间：
2012-11
期刊：
影响因子：
2.1
通讯作者：
Xu Y
中科院分区：
文献类型：
--
作者：
Krol A;Li S;Shen L;Xu Y
我们提出了一种预处理交替投影算法（PAPA）来解决最大后验（MAP）发射计算机断层扫描（ECT）重建问题。具体来说，我们将重构问题表述为一个具有全变分（TV）正则化的约束凸优化问题。然后，我们描述了约束凸优化问题的解，并证明它满足一个由两个邻近算子定义的不动点方程组，这些算子由定义问题中涉及的tv范数和约束的凸函数提出。通过定义两个投影算子的接近算子来表征（解）自然会导致寻找解的交替投影算法。为了高效的数值计算，我们在交替投影算法中引入了优化问题中密集系统矩阵的预处理矩阵（em - preconditioning）。我们从理论上证明了PAPA的收敛性。在数值实验中，我们的算法在适当选择预处理矩阵的情况下，与传统的带有电视正则化器（EM-TV）的MAP期望最大化（MAP- em）算法和最近开发的用于ECT重建的嵌套EM-TV算法的性能进行了比较。通过数值实验，我们观察到带有em - pre调节器的交替投影算法在收敛速度、重建图像中的噪声和图像质量等方面都明显优于EM-TV算法。它在收敛速度上也优于嵌套EM-TV，同时提供相当的图像质量。
We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.
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影响因子：
10.6
作者：
HEBERT, T;LEAHY, R
通讯作者：
LEAHY, R
影响因子：
2.1
作者：
Bonettini, S.;Ruggiero, V.
通讯作者：
Ruggiero, V.
影响因子：
2.1
作者：
Byrne, C
通讯作者：
Byrne, C
DOI：
10.1364/josaa.7.001266
发表时间：
1990-07-01
影响因子：
1.9
作者：
BARRETT, HH
通讯作者：
BARRETT, HH
影响因子：
10.6
作者：
FESSLER, JA
通讯作者：
FESSLER, JA