Joint Diffusion: Mutual Consistency-Driven Diffusion Model for PET-MRI Co-Reconstruction

TL;DR

This work introduces MC-Diffusion, a mutual consistency-driven diffusion model for joint PET-MRI reconstruction. By learning the joint distribution $P(\mathbf{u},\mathbf{v})$ via a time-dependent score network $\mathbf{s}_{\theta}(\mathbf{X},t)$ and integrating data-fidelity terms from both PET and MRI forward models, MC-Diffusion performs joint sampling using a predictor-corrector scheme within a diffusion framework. Experiments on the ADNI dataset demonstrate that MC-Diffusion outperforms traditional joint-reconstruction methods and supervised DL baselines in terms of NMSE, PSNR, and SSIM across multiple undersampling scenarios, highlighting the value of cross-modal information. The approach advances PET-MRI reconstruction by explicitly modeling the joint probability distribution to capture complementary information beyond structural similarity, with practical impact in accelerated MRI and improved PET image quality. Future work includes exploring alternative score-architecture designs beyond U-Net to further enhance joint priors and generalization.

Abstract

Positron Emission Tomography and Magnetic Resonance Imaging (PET-MRI) systems can obtain functional and anatomical scans. PET suffers from a low signal-to-noise ratio. Meanwhile, the k-space data acquisition process in MRI is time-consuming. The study aims to accelerate MRI and enhance PET image quality. Conventional approaches involve the separate reconstruction of each modality within PET-MRI systems. However, there exists complementary information among multi-modal images. The complementary information can contribute to image reconstruction. In this study, we propose a novel PET-MRI joint reconstruction model employing a mutual consistency-driven diffusion mode, namely MC-Diffusion. MC-Diffusion learns the joint probability distribution of PET and MRI for utilizing complementary information. We conducted a series of contrast experiments about LPLS, Joint ISAT-net and MC-Diffusion by the ADNI dataset. The results underscore the qualitative and quantitative improvements achieved by MC-Diffusion, surpassing the state-of-the-art method.

Figures (6)

• Figure 1: The scheme of MC-Diffusion. (a) In the forward process, noise at different scales is gradually added into the multi-modality and conducted Langevin MCMC sampling in the reverse process. (b) The same noise added into mutual consistency PET and MRI in the forward process.
• Figure 2: Reconstruction results under cartesian undersampling at 4-fold. The values in the corner are each slice's PSNR/SSIM/NMSE values. The first row describes the ground truth of MRI and the results of reconstruction by independent model and joint reconstruction model. The second row shows MRI undersampling patterns and error views. The grayscale of the reconstructed images and the error images' colour bar are on the figure's right.
• Figure 3: Reconstruction results for sinograms of size $128 \times 300$. The first row describes the ground truth of PET and the results of reconstruction by independent model and joint reconstruction model. The second row shows PET sinogram data and error views.
• Figure 4: Joint reconstruction results under cartesian undersampling at 3-fold and for sinograms of size $128 \times 300$. The values in the corner are each slice's PSNR/SSIM/NMSE values. The first row describes the ground truth of MRI and the results of reconstruction by contrast models. The second row shows MRI undersampling patterns and error views. The third row describes the ground truth of PET and the results of joint reconstruction by contrast models. The fourth row shows PET sinogram data and error views. The grayscale of the reconstructed images and the error images' colour bar are on the figure's right.
• Figure 5: Joint reconstruction results under cartesian undersampling at 4-fold and for sinograms of size $128 \times 300$. The first row describes the ground truth of MRI and the results of reconstruction by contrast models. The second row shows MRI subsampling patterns and error views. The third row describes the ground truth of PET and the results of joint reconstruction by contrast models. The fourth row shows PET sinogram data and error views.