多核和多核空间正则化的PET图像重建
PET Image Reconstruction with Multiple Kernels and Multiple Kernel Space Regularizers
摘要：
核化最大似然（ML）期望最大化（EM）方法最近在PET图像重建中获得了突出地位，优于许多先前的最先进的方法。但它们也不能避免非核化MLEM方法存在的潜在重建误差大和对迭代次数敏感等问题。本文通过理论推导和实验结果对这些问题进行了论证，并提出了一种新的解决方案。该解决方案是一个正则化核MLEM与多个核矩阵和多个核空间正则化，可以针对不同的应用程序。为了减小重建误差和对迭代次数的敏感性，本文提出了一类多核矩阵和由核图像字典和核图像Laplacian四元数构成的正则化子，并利用它们分别推导了单核正则化EM和多核正则化EM算法，用于PET图像重建。这些新算法是利用机器学习中的多核组合、稀疏编码中的图像字典学习和图信号处理中的图拉普拉斯二次型等技术工具推导出来的。对模拟数据和体内数据进行了广泛的测试和比较，以验证和评估新算法，并证明其优越的性能和优势，比内核化的MLEM和其他传统方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
