Fessler J A, Ficaro E P, Clinthorne N H, Lange K
University of Michigan, Ann Arbor 48109-2122, USA.
IEEE Trans Med Imaging. 1997 Apr;16(2):166-75. doi: 10.1109/42.563662.
This paper presents a new class of algorithms for penalized-likelihood reconstruction of attenuation maps from low-count transmission scans. We derive the algorithms by applying to the transmission log-likelihood a version of the convexity technique developed by De Pierro for emission tomography. The new class includes the single-coordinate ascent (SCA) algorithm and Lange's convex algorithm for transmission tomography as special cases. The new grouped-coordinate ascent (GCA) algorithms in the class overcome several limitations associated with previous algorithms. 1) Fewer exponentiations are required than in the transmission maximum likelihood-expectation maximization (ML-EM) algorithm or in the SCA algorithm. 2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradient-based methods. 3) The algorithms are easily parallelizable, unlike the SCA algorithm and perhaps line-search algorithms. We show that the GCA algorithms converge faster than the SCA algorithm, even on conventional workstations. An example from a low-count positron emission tomography (PET) transmission scan illustrates the method.
本文提出了一类新的算法，用于从低计数透射扫描中进行惩罚似然重建衰减图。我们通过将De Pierro为发射断层扫描开发的凸性技术的一个版本应用于透射对数似然来推导这些算法。新的类别包括单坐标上升（SCA）算法和Lange用于透射断层扫描的凸算法作为特殊情况。该类别中的新分组坐标上升（GCA）算法克服了与先前算法相关的几个限制。1）与透射最大似然期望最大化（ML-EM）算法或SCA算法相比，所需的指数运算更少。2）与许多基于梯度的方法不同，这些算法本质上适应非负约束。3）与SCA算法以及可能的线搜索算法不同，这些算法易于并行化。我们表明，即使在传统工作站上，GCA算法也比SCA算法收敛得更快。来自低计数正电子发射断层扫描（PET）透射扫描的一个例子说明了该方法。
