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arXiv 1803.01112physics.med-phcs.CYmath.OC
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一种改进的全变分优化方法在质子计算机断层成像重建中的应用

An Improved Method of Total Variation Superiorization Applied to Reconstruction in Proton Computed Tomography

Blake Schultze, Yair Censor, Paniz Karbasi, Keith E. Schubert, Reinhard W. Schulte

摘要:

以前的工作表明,全变差优化(TVS)提高了质子计算机断层成像(pCT)的重建图像质量。从那时起,TVS算法的结构不断发展,这项工作研究了这种新的算法结构是否为pCT图像质量提供了额外的好处。引入到原始TVS算法的结构和参数变化包括:(1)包括或排除TV减少要求,(2)每个可行性搜索迭代的TV扰动步骤的可变数量$N$,以及(3)引入扰动核$0<α<1$。排除TV降低要求检查的结构变化往往对$3\le N\le 6$有有益影响,并允许TVS算法完全并行化。每次可行性搜索迭代的重复扰动降低了$3\le N\le 6$的总变差(TV)和材料相关标准差。扰动核$α$(相当于原始TVS算法中的$α=0.5$)在$α$增加超过$α=0.5$时降低了TV和标准偏差,但对$α>0.75$的重建相对阻止力(RSP)值产生了负面影响。TV和标准差的降低允许使用比以前使用的更大的松弛参数$λ$进行可行性搜索,而不会出现原始TVS算法所经历的标准差的相应增加。这项工作表明,与原始TVS算法的演变相关的修改在适当选择的参数值的pCT图像质量和计算效率方面提供了益处。

英文摘要:

Previous work showed that total variation superiorization (TVS) improves reconstructed image quality in proton computed tomography (pCT). The structure of the TVS algorithm has evolved since then and this work investigated if this new algorithmic structure provides additional benefits to pCT image quality. Structural and parametric changes introduced to the original TVS algorithm included: (1) inclusion or exclusion of TV reduction requirement, (2) a variable number, $N$, of TV perturbation steps per feasibility-seeking iteration, and (3) introduction of a perturbation kernel $0<α<1$. The structural change of excluding the TV reduction requirement check tended to have a beneficial effect for $3\le N\le 6$ and allows full parallelization of the TVS algorithm. Repeated perturbations per feasibility-seeking iterations reduced total variation (TV) and material dependent standard deviations for $3\le N\le 6$. The perturbation kernel $α$, equivalent to $α=0.5$ in the original TVS algorithm, reduced TV and standard deviations as $α$ was increased beyond $α=0.5$, but negatively impacted reconstructed relative stopping power (RSP) values for $α>0.75$. The reductions in TV and standard deviations allowed feasibility-seeking with a larger relaxation parameter $λ$ than previously used, without the corresponding increases in standard deviations experienced with the original TVS algorithm. This work demonstrates that the modifications related to the evolution of the original TVS algorithm provide benefits in terms of both pCT image quality and computational efficiency for appropriately chosen parameter values.

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