Exploiting network optimization stability for enhanced PET image denoising using deep image prior

<i>Objective</i>. Positron emission tomography (PET) is affected by statistical noise due to constraints on tracer dose and scan duration, impacting both diagnostic performance and quantitative accuracy. While deep learning-based PET denoising methods have been used to improve image quality, they may introduce over-smoothing, which can obscure critical structural details and compromise quantitative accuracy. We propose a method for making a deep learning solution more reliable and apply it to the conditional deep image prior (DIP).<i>Approach</i>. We introduce the idea of<i>stability information</i>in the optimization process of conditional DIP, enabling the identification of unstable regions within the network's optimization trajectory. Our method incorporates a stability map, which is derived from multiple intermediate outputs of a moderate neural network at different optimization steps. The final denoised PET image is then obtained by computing a linear combination of the DIP output and the original reconstructed PET image, weighted by the stability map.<i>Main results</i>. We employed eight high-resolution brain PET datasets for comparison. Our method effectively reduces background noise while preserving small structure details in brain [¹⁸F]FDG PET images. Comparative analysis demonstrated that our approach outperformed existing methods in terms of peak-to-valley ratio and background noise suppression across various low-dose levels. Additionally, region-of-interest analysis confirmed that the proposed method maintains quantitative accuracy without introducing under- or over-estimation. Furthermore, we applied our method to full-dose PET data to assess its impact on image quality. The results revealed that the proposed method significantly reduced background noise while preserving the peak-to-valley ratio at a level comparable to that of unfiltered full-dose PET images.<i>Significance</i>. The proposed method introduces a robust approach to deep learning-based PET denoising, enhancing its reliability and preserving quantitative accuracy. Furthermore, this strategy can potentially advance performance in high-sensitivity PET scanners and surpass the limit of image quality inherent to PET scanners.