PET Image Reconstruction with Kernel and Kernel Space Composite Regularizer

<div>Represented by the kernelized expectation maximization (KEM), the 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 variance and high sensitivity to iteration number. Also, it is generally difficult to simultaneously reduce image variance and preserve image details using kernels. To solve these problems, this paper presents a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smoothes the kernel coefficients, a non-convex kernel space energy regularizer that enhances the coefficients’ energy, and a composition constant that guarantees the convexity of composite regularizer. These kernel space regularizers are based on the theory of data manifold and graph regularization and can be constructed from different prior image data for simultaneous image variance reduction and image detail preservation. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.</div>