A splitting-based iterative algorithm for accelerated statistical X-ray CT reconstruction.
A splitting-based iterative algorithm for accelerated statistical X-ray CT reconstruction.
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DOI：
10.1109/tmi.2011.2175233
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发表时间：
2012-03
影响因子：
10.6
通讯作者：
Fessler JA
中科院分区：
文献类型：
--
作者：
Ramani S;Fessler JA
使用惩罚加权最小二乘 (PWLS) 标准进行统计图像重建可以提高 X 射线 CT 的图像质量。然而，统计权重的巨大动态范围导致了高度移位变异的逆问题，使得很难预处理和加速直接攻击统计模型的现有迭代算法。我们建议通过使用变量分割方案来缓解这个问题，该方案将统计数据模型的平移变量和（“几乎”）不变分量分开，并且还解耦正则化项。这导致了一个等效的约束问题，我们使用具有交替最小化的经典乘法器框架来解决该问题。我们的分裂的具体形式产生了一种交替方向乘法器（ADMM）算法，其内部步骤涉及“几乎”平移不变的线性系统，适合使用锥形滤波器进行基于 FFT 的预处理。所提出的方法可以有效地处理各种凸正则化标准，包括基于 ℓ1 范数和总变分的平滑边缘保持正则化器和非平滑稀疏性促进正则化器。使用合成和真实体内人体数据进行的数值实验表明，与适用于 CT 的传统算法（非线性共轭梯度、有序子集）和最先进的算法（MFISTA、split-Bregman）相比，锥形滤波器预处理器加速了所提出的 ADMM，从而导致 ADMM 快速收敛。
Statistical image reconstruction using penalized weighted least-squares (PWLS) criteria can improve image-quality in X-ray CT. However, the huge dynamic range of the statistical weights leads to a highly shift-variant inverse problem making it difficult to precondition and accelerate existing iterative algorithms that attack the statistical model directly. We propose to alleviate the problem by using a variable-splitting scheme that separates the shift-variant and (“nearly”) invariant components of the statistical data model and also decouples the regularization term. This leads to an equivalent constrained problem that we tackle using the classical method-of-multipliers framework with alternating minimization. The specific form of our splitting yields an alternating direction method of multipliers (ADMM) algorithm with an inner-step involving a “nearly” shift-invariant linear system that is suitable for FFT-based preconditioning using cone-type filters. The proposed method can efficiently handle a variety of convex regularization criteria including smooth edge-preserving regularizers and nonsmooth sparsity-promoting ones based on the ℓ1-norm and total variation. Numerical experiments with synthetic and real in vivo human data illustrate that cone-filter preconditioners accelerate the proposed ADMM resulting in fast convergence of ADMM compared to conventional (nonlinear conjugate gradient, ordered subsets) and state-of-the-art (MFISTA, split-Bregman) algorithms that are applicable for CT.