Deep denoiser prior driven relaxed iterated Tikhonov method for low-count PET image restoration

Objective. Low-count positron emission tomography (PET) imaging is an efficient way to promote more widespread use of PET because of its short scan time and low injected activity. However, this often leads to low-quality PET images with clinical image reconstruction, due to high noise and blurring effects. Existing PET image restoration (IR) methods hinder their own restoration performance due to the semi-convergence property and the lack of suitable denoiser prior.Approach. To overcome these limitations, we propose a novel deep plug-and-play IR method called Deep denoiser Prior driven Relaxed Iterated Tikhonov method (DP-RI-Tikhonov). Specifically, we train a deep convolutional neural network denoiser to generate a flexible deep denoiser prior to handle high noise. Then, we plug the deep denoiser prior as a modular part into a novel iterative optimization algorithm to handle blurring effects and propose an adaptive parameter selection strategy for the iterative optimization algorithm.Main results. Simulation results show that the deep denoiser prior plays the role of reducing noise intensity, while the novel iterative optimization algorithm and adaptive parameter selection strategy can effectively eliminate the semi-convergence property. They enable DP-RI-Tikhonov to achieve an average quantitative result (normalized root mean square error, structural similarity) of (0.1364, 0.9574) at the stopping iteration, outperforming a conventional PET IR method with an average quantitative result of (0.1533, 0.9523) and a state-of-the-art deep plug-and-play IR method with an average quantitative result of (0.1404, 0.9554). Moreover, the advantage of DP-RI-Tikhonov becomes more obvious at the last iteration. Experiments on six clinical whole-body PET images further indicate that DP-RI-Tikhonov successfully reduces noise intensity and recovers fine details, recovering sharper and more uniform images than the comparison methods.Significance. DP-RI-Tikhonov's ability to reduce noise intensity and effectively eliminate the semi-convergence property overcomes the limitations of existing methods. This advancement may have substantial implications for other medical IR.