A unified approach to statistical tomography using coordinate descent optimization
A unified approach to statistical tomography using coordinate descent optimization
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DOI：
10.1109/83.491321
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发表时间：
1996-03-01
影响因子：
10.6
通讯作者：
Sauer, K
中科院分区：
文献类型：
--
作者：
Bouman, CA;Sauer, K
在过去的十年中，有相当大的兴趣在统计上最佳重建断层数据的横截面图像。特别地，已经提出了各种这样的算法用于从发射断层扫描数据的最大后验（MAP）重建。虽然MAP估计需要最优化问题的解，但是大多数现有的重建算法采用基于期望最大化（EM）算法的间接方法。我们提出了一种基于MAP准则的直接优化的统计最优图像重建的新方法，这种直接优化方法的关键是贪婪的逐像素计算，称为迭代坐标下降（ICD）。我们提出了一种新的方法来计算ICD更新，我们称之为ICD/牛顿-拉夫森。我们表明，ICD/Newton-Raphson需要近似相同的计算量，每次迭代的EM为基础的方法，但新的方法收敛得更快（在我们的实验中，通常为5至10次迭代），ICD/Newton-Raphson方法的其他优点是，它很容易应用到MAP估计的传输断层图像，和典型的凸约束，如积极性，很容易纳入。
Over the past ten years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data, While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm, In this paper, we propose a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion, The key to this direct optimization approach is greedy pixel-wise computations known as iterative coordinate decent (ICD). We propose a novel method for computing the ICD updates, which we call ICD/Newton-Raphson. We show that ICD/Newton-Raphson requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly (in our experiments, typically five to ten iterations), Other advantages of the ICD/Newton-Raphson method are that it is easily applied to MAP estimation of transmission tomograms, and typical convex constraints, such as positivity, are easily incorporated.