Kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction error and high sensitivity to iteration number. This paper demonstrates these problems by theoretical reasoning and experiment results, and provides a novel solution to solve these problems. The solution is a regularized kernelized MLEM with multiple kernel matrices and multiple kernel space regularizers that can be tailored for different applications. To reduce the reconstruction error and the sensitivity to iteration number, we present a general class of multi-kernel matrices and two regularizers consisting of kernel image dictionary and kernel image Laplacian quatradic, and use them to derive the single-kernel regularized EM and multi-kernel regularized EM algorithms for PET image reconstruction. These new algorithms are derived using the technical tools of multi-kernel combination in machine learning, image dictionary learning in sparse coding, and graph Laplcian quadratic in graph signal processing. Extensive tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the new algorithms, and demonstrate their superior performance and advantages over the kernelized MLEM and other conventional methods.

翻译：最近,在PET图像重建中,最大近似内脏(ML)最大预期最大化(EM)方法在PET图像重建中占据了突出地位,超过了以往许多最先进的方法。但是,在潜在的重建大错误和对迭代号的高度敏感度中,这些方法并非不受非内脏的MLEM方法问题的影响。本文通过理论推理和实验结果展示了这些问题,并提供了解决这些问题的新的解决办法。解决方案是常规电离和多内核标准化的EM算法,为PET图像重建提供了一种正规化的MLEM内脏和多内核空间管理器。为了减少重建错误和对迭代数的敏感度,我们提出了一个多内层矩阵和两种非内脏MLEM内脏方法的一般类别和两种正规化方法,包括内脏图像字典和内脏图像平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面图。这些新算法是利用机器学习、图像学习、图像平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面。