Double-Constraint Diffusion Model with Nuclear Regularization for Ultra-low-dose PET Reconstruction

Ultra-low-dose positron emission tomography (PET) reconstruction holds significant potential for reducing patient radiation exposure and shortening examination times. However, it may also lead to increased noise and reduced imaging detail, which could decrease the image quality. In this study, we present a Double-Constraint Diffusion Model (DCDM), which freezes the weights of a pre-trained diffusion model and injects a trainable double-constraint controller into the encoding architecture, greatly reducing the number of trainable parameters for ultra-low-dose PET reconstruction. Unlike full fine-tuning models, DCDM can adapt to different dose levels without retraining all model parameters, thereby improving reconstruction flexibility. Specifically, the two constraint modules, named the Nuclear Transformer Constraint (NTC) and the Encoding Nexus Constraint (ENC), serve to refine the pre-trained diffusion model. The NTC leverages the nuclear norm as an approximation for matrix rank minimization, integrates the low-rank property into the Transformer architecture, and enables efficient information extraction from low-dose images and conversion into compressed feature representations in the latent space. Subsequently, the ENC utilizes these compressed feature representations to encode and control the pre-trained diffusion model, ultimately obtaining reconstructed PET images in the pixel space. In clinical reconstruction, the compressed feature representations from NTC help select the most suitable ENC for efficient unknown low-dose PET reconstruction. Experiments conducted on the UDPET public dataset and the Clinical dataset demonstrated that DCDM outperforms state-of-the-art methods on known dose reduction factors (DRF) and generalizes well to unknown DRF scenarios, proving valuable even at ultra-low dose levels, such as 1% of the full dose.