Fast PET imaging is clinically important for reducing motion artifacts and improving patient comfort. While recent diffusion-based deep learning methods have shown promise, they often fail to capture the true PET degradation process, suffer from accumulated inference errors, introduce artifacts, and require extensive reconstruction iterations. To address these challenges, we propose a novel multistage diffusion framework tailored for fast PET imaging. At the coarse level, we design a multistage structure to approximate the temporal non-linear PET degradation process in a data-driven manner, using paired PET images collected under different acquisition duration. A Phase Error Correction Network (PECNet) ensures consistency across stages by correcting accumulated deviations. At the fine level, we introduce a deterministic cold diffusion mechanism, which simulates intra-stage degradation through interpolation between known acquisition durations—significantly reducing reconstruction iterations to as few as 10. Evaluations on [68Ga]FAPI and [18F]FDG PET datasets demonstrate the superiority of our approach, achieving peak PSNRs of 36.2 dB and 39.0 dB, respectively, with average SSIMs over 0.97. Our framework offers high-fidelity PET imaging with fewer iterations, making it practical for accelerated clinical imaging.

Integrating knowledge into text is a promising way to enrich text representation, especially in the medical field.However, undifferentiated knowledge not only confuses the text representation but also imports unexpected noises.In this paper, to alleviate this problem, we propose leveraging capsule routing to associate knowledge with medical literature hierarchically (called HiCapsRKL).Firstly, HiCapsRKL extracts two empirically designed text fragments from medical literature and encodes them into fragment representations respectively.Secondly, the capsule routing algorithm is applied to two fragment representations.Through the capsule computing and dynamic routing, each representation is processed into a new representation (denoted as caps-representation), and we integrate the caps-representations as information gain to associate knowledge with medical literature hierarchically.Finally, HiCapsRKL are validated on relevance prediction and medical literature retrieval test sets.The experimental results and analyses show that HiCapsRKL can more accurately associate knowledge with medical literature than the mainstream methods.In summary, HiCapsRKL can efficiently help selecting the most relevant knowledge to the medical literature, which may be an alternative attempt to improve knowledge-based text representation.Source code is released on GitHub 1 .