A Bi-level Optimization Model with Multi-kernel and Diffusion Regularization for PET Image Reconstruction

Image reconstruction in positron emission tomography (PET) is essential for disease diagnosis and treatment evaluation, but it struggles with noise and inadequate image quality. The traditional kernel expectation maximization (KEM) algorithm uses prior information to improve reconstruction quality and offers computational simplicity. However, its fixed kernel forms, noise sensitivity, and limited flexibility might adversely affect the accuracy and robustness of the reconstructed images. In this study, we propose a bi-level optimization model that alternately refines a multi-kernel matrix and a diffusion coefficient prior to capture non-linear mappings from projection data. Specifically, we employ a pre-trained score-based diffusion model to achieve improved noise suppression and detail recovery. Guided by reverse stochastic differential equations, this model effectively captures the complex distribution. Additionally, a multi-kernel strategy combining radial Gaussian and polynomial kernels is utilized to enhance the optimization of the kernel matrix. Experimental results across multiple datasets demonstrated that the pro-posed model outperformed existing kernel-related methods in dynamic PET reconstruction. Preliminary clinical experiments under a one-half-count, slice-wise 2D setting demonstrated the feasibility of the proposed framework, while more severe count-reduction and fully 3D evaluations remain necessary.