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

arXiv: https://arxiv.org/abs/2509.00395 · HTML: https://mlsanity.com/paper/2509.00395/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 30 Aug 2025.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 25 of 25)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [White-Box Transformers via Sparse Rate Reduction](https://mlsanity.com/paper/2306.01129/) (2023)
- [PET image denoising based on denoising diffusion probabilistic models](https://mlsanity.com/paper/2209.06167/) (2022)
- [Iterative PET Image Reconstruction Using Convolutional Neural Network Representation](https://mlsanity.com/paper/1710.03344/) (2017)
- [200x Low-dose PET Reconstruction using Deep Learning](https://mlsanity.com/paper/1712.04119/) (2017)
- [Contrastive Diffusion Model with Auxiliary Guidance for Coarse-to-Fine PET Reconstruction](https://mlsanity.com/paper/2308.10157/) (2023)
- [Full-dose Whole-body PET Synthesis from Low-dose PET Using High-efficiency Denoising Diffusion Probabilistic Model: PET Consistency Model](https://mlsanity.com/paper/2308.13072/) (2023)
- [Diff-Restorer: Unleashing Visual Prompts for Diffusion-based Universal Image Restoration](https://mlsanity.com/paper/2407.03636/) (2024)
- [Synthesizing PET images from High-field and Ultra-high-field MR images Using Joint Diffusion Attention Model](https://mlsanity.com/paper/2305.03901/) (2023)
- [Joint Diffusion: Mutual Consistency-Driven Diffusion Model for PET-MRI Co-Reconstruction](https://mlsanity.com/paper/2311.14473/) (2023)
- [Brain PET Synthesis from MRI Using Joint Probability Distribution of Diffusion Model at Ultrahigh Fields](https://mlsanity.com/paper/2211.08901/) (2022)
- [Diffusion Transformer Model With Compact Prior for Low-dose PET Reconstruction](https://mlsanity.com/paper/2407.00944/) (2024)

## Abstract (arXiv)

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.