Kernel-based curve-fitting method with spatial regularization for generation of parametric images in dynamic PET

Due to high levels of noise in pixel-wise time-activity curves, the indirect method that generates kinetic parametric images from dynamic positron emission tomography (PET) images often results in poor parametric image quality. We have demonstrated that the quality of parametric images can be improved by denoising dynamic PET images, using gradient-free curve-fitting and applying a kernel-based post-filtering to parametric images. However, many gradient-free curve-fitting methods are time-consuming. Moreover, some parameter estimates (e.g. k₂ and k₃) have large variability. To provide high-quality PET parametric images with low computational cost, we propose a curve-fitting method that incorporates the kernel-based denoising method and the highly constrained backprojection technique into the Levenberg-Marquardt (LM) algorithm. We conducted a simulation study to evaluate the performance of the proposed curve-fitting method. Dynamic PET images were reconstructed using the expectation-maximization (EM) algorithm and were denoised before parameter estimation. Compared to the LM algorithm with and without the kernel-based post-filtering, the proposed method achieved superior performance, offering a decrease in both bias and coefficient of variation (CV) on all parametric images. Overall, the proposed method exhibited lower bias and slightly higher CV than the gradient-free pattern search method with the kernel-based post-filtering (PatS-K). Moreover, the computation time of the proposed method was about 18 times lower than that of the PatS-K method. Finally, we show that the proposed method can further improve the quality of parametric images when dynamic PET images are reconstructed using the kernel-based EM algorithm.