Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN.
IEEE Trans Image Process. 1996;5(3):480-92. doi: 10.1109/83.491321.
Over the past 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. 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.
在过去的几年中，人们对从层析数据中统计最优地重建横截面图像产生了浓厚的兴趣。特别是，已经提出了多种用于从发射层析数据进行最大后验 (MAP) 重建的算法。虽然 MAP 估计需要求解优化问题，但大多数现有的重建算法都采用基于期望最大化 (EM) 算法的间接方法。我们提出了一种新的基于直接优化 MAP 准则的统计最优图像重建方法。这种直接优化方法的关键是称为迭代坐标下降 (ICD) 的贪婪逐像素计算。我们提出了一种用于计算 ICD 更新的新方法，我们称之为 ICD/Newton-Raphson。我们表明，ICD/Newton-Raphson 每迭代所需的计算量与基于 EM 的方法大致相同，但新方法的收敛速度要快得多（在我们的实验中，通常需要五到十次迭代）。ICD/Newton-Raphson 方法的其他优点是它易于应用于透射层析图的 MAP 估计，并且可以轻松合并典型的凸约束，例如正定性。
