  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.
