PET Image Reconstruction with Multiple Kernels and Multiple Kernel Space Regularizers

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.