A Krasnoselskii-Mann Algorithm With an Improved EM Preconditioner for PET Image Reconstruction.
A Krasnoselskii-Mann Algorithm With an Improved EM Preconditioner for PET Image Reconstruction.
复制标题
具有改进的 EM 预处理器的 Krasnoselskii-Mann 算法用于 PET 图像重建
DOI：
10.1109/tmi.2019.2898271
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发表时间：
2019-09
影响因子：
10.6
通讯作者：
Xu Y
中科院分区：
文献类型：
--
作者：
Lin Y;Schmidtlein CR;Li Q;Li S;Xu Y
提出了一种改进EM预处理器的预处理Krasnoselskiii-Mann（KM）算法（IEM-PKMA），用于高阶全变分（HOTV）正则化正电子发射断层扫描（PET）图像重建。PET重建问题可以用公式表示为三项凸优化模型，该模型由Kullback-Leibler（KL）保真度项、非光滑惩罚项和非负约束项（也是非光滑的）组成。我们开发了一个有效的KM算法解决这个优化问题的基础上，其解决方案的不动点表征，与预条件和动量技术加速收敛。通过结合EM预处理器，阈值，和一个很好的廉价的估计的解决方案，我们提出了一种改进的EM预处理器，不仅可以加速收敛，但也避免重建图像被“卡在零”。数值结果表明，本文提出的IEM-PKMA算法在求解各向异性光滑全变分正则化模型时，性能优于现有的优化转移下降算法和预条件L-BFGS-B算法，在求解不可微HOTV正则化模型时，性能优于预条件交替投影算法和乘子交替方向法.令人鼓舞的初步实验，使用临床数据。
This paper presents a preconditioned Krasnoselskii-Mann (KM) algorithm with an improved EM preconditioner (IEM-PKMA) for higher-order total variation (HOTV) regularized positron emission tomography (PET) image reconstruction. The PET reconstruction problem can be formulated as a three-term convex optimization model consisting of the Kullback–Leibler (KL) fidelity term, a nonsmooth penalty term, and a nonnegative constraint term which is also nonsmooth. We develop an efficient KM algorithm for solving this optimization problem based on a fixed-point characterization of its solution, with a preconditioner and a momentum technique for accelerating convergence. By combining the EM precondtioner, a thresholding, and a good inexpensive estimate of the solution, we propose an improved EM preconditioner that can not only accelerate convergence but also avoid the reconstructed image being “stuck at zero.” Numerical results in this paper show that the proposed IEM-PKMA outperforms existing state-of-the-art algorithms including, the optimization transfer descent algorithm and the preconditioned L-BFGS-B algorithm for the differentiable smoothed anisotropic total variation regularized model, the preconditioned alternating projection algorithm, and the alternating direction method of multipliers for the nondifferentiable HOTV regularized model. Encouraging initial experiments using clinical data are presented.