Joint diffusion: mutual consistency-driven diffusion model for PET-MRI co-reconstruction.

Objective. Positron Emission Tomography and Magnetic Resonance Imaging (PET-MRI) systems can obtain functional and anatomical scans. But PET suffers from a low signal-to-noise ratio, while MRI are time-consuming. To address time-consuming, an effective strategy involves reducing k-space data collection, albeit at the cost of lowering image quality. This study aims to leverage the inherent complementarity within PET-MRI data to enhance the image quality of PET-MRI.Approach. A novel PET-MRI joint reconstruction model, termed MC-Diffusion, is proposed in the Bayesian framework. The joint reconstruction problem is transformed into a joint regularization problem, where data fidelity terms of PET and MRI are expressed independently. The regular term, the derivative of the logarithm of the joint probability distribution of PET and MRI, employs a joint score-based diffusion model for learning. The diffusion model involves the forward diffusion process and the reverse diffusion process. The forward diffusion process adds noise to transform a complex joint data distribution into a known joint prior distribution for PET and MRI simultaneously, resembling a denoiser. The reverse diffusion process removes noise using a denoiser to revert the joint prior distribution to the original joint data distribution, effectively utilizing joint probability distribution to describe the correlations of PET and MRI for improved quality of joint reconstruction.Main results. Qualitative and quantitative improvements are observed with the MC-Diffusion model. Comparative analysis against LPLS and Joint ISAT-net on the ADNI dataset demonstrates superior performance by exploiting complementary information between PET and MRI. The MC-Diffusion model effectively enhances the quality of PET and MRI images.Significance. This study employs the MC-Diffusion model to enhance the quality of PET-MRI images by integrating the fundamental principles of PET and MRI modalities and leveraging their inherent complementarity. Furthermore, utilizing the diffusion model to learn the joint probability distribution of PET and MRI, thereby elucidating their latent correlation, facilitates a more profound comprehension of the priors obtained through deep learning, contrasting with black-box prior or artificially constructed structural similarities.

Synthesizing PET images from high-field and ultra-high-field MR images using joint diffusion attention model.

BACKGROUND: Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET) stand as pivotal diagnostic tools for brain disorders, offering the potential for mutually enriching disease diagnostic perspectives. However, the costs associated with PET scans and the inherent radioactivity have limited the widespread application of PET. Furthermore, it is noteworthy to highlight the promising potential of high-field and ultra-high-field neuroimaging in cognitive neuroscience research and clinical practice. With the enhancement of MRI resolution, a related question arises: can high-resolution MRI improve the quality of PET images? PURPOSE: This study aims to enhance the quality of synthesized PET images by leveraging the superior resolution capabilities provided by high-field and ultra-high-field MRI. METHODS: From a statistical perspective, the joint probability distribution is considered the most direct and fundamental approach for representing the correlation between PET and MRI. In this study, we proposed a novel model, the joint diffusion attention model, namely, the joint diffusion attention model (JDAM), which primarily focuses on learning information about the joint probability distribution. JDAM consists of two primary processes: the diffusion process and the sampling process. During the diffusion process, PET gradually transforms into a Gaussian noise distribution by adding Gaussian noise, while MRI remains fixed. The central objective of the diffusion process is to learn the gradient of the logarithm of the joint probability distribution between MRI and noise PET. The sampling process operates as a predictor-corrector. The predictor initiates a reverse diffusion process, and the corrector applies Langevin dynamics. RESULTS: Experimental results from the publicly available Alzheimer's Disease Neuroimaging Initiative dataset highlight the effectiveness of the proposed model compared to state-of-the-art (SOTA) models such as Pix2pix and CycleGAN. Significantly, synthetic PET images guided by ultra-high-field MRI exhibit marked improvements in signal-to-noise characteristics when contrasted with those generated from high-field MRI data. These results have been endorsed by medical experts, who consider the PET images synthesized through JDAM to possess scientific merit. This endorsement is based on their symmetrical features and precise representation of regions displaying hypometabolism, a hallmark of Alzheimer's disease. CONCLUSIONS: This study establishes the feasibility of generating PET images from MRI. Synthesis of PET by JDAM significantly enhances image quality compared to SOTA models.

DPP: deep phase prior for parallel imaging with wave encoding.

Objective.In Magnetic Resonance (MR) parallel imaging with virtual channel-expanded Wave encoding, limitations are imposed on the ability to comprehensively and accurately characterize the background phase. These limitations are primarily attributed to the calibration process relying solely on center low-frequency Auto-Calibration Signals (ACS) data for calibration.Approach.To tackle the challenge of accurately estimating the background phase in wave encoding, a novel deep neural network model guided by deep phase priors is proposed with integrated virtual conjugate coil (VCC) extension. Concretely, within the proposed framework, the background phase is implicitly characterized by employing a carefully designed decoder convolutional neural network, leveraging the inherent characteristics of phase smoothness and compact support in the transformed domain. Furthermore, the proposed model with wave encoding benefits from additional priors, which incorporate transmission sparsity of the latent image and coil sensitivity smoothness.Main results.Ablation experiments were conducted to ascertain the proposed method's capability to implicitly represent CSM and the background phase. Subsequently, the superiority of the proposed method is demonstrated through confidence comparisons with competing methods, employing 4-fold and 5-fold acceleration experiments. In achieving 4-fold and 5-fold acceleration, the optimal quantitative metrics (PSNR/SSIM/NMSE) are 44.1359 dB/0.9863/0.0008 (4-fold) and 41.2074/0.9846/0.0017 (5-fold), respectively. Furthermore, the generalizability of the proposed method is further validated by conducting acceleration experiments with T1, T2, T2*, and various undersampling patterns. In addition, the DPP delivered much better performance than the conventional methods by exploring accelerated phase-sensitive SWI imaging. In SWI accelerated imaging, it also surpasses the optimal competing method in terms of (PSNR/SSIM/NMSE) with 0.096%/0.009%/0.0017%.Significance.The proposed method enables precise characterization of the background phase in the integrated VCC and wave encoding framework, supported via theoretical analysis and empirical findings. Our code is available at:https://github.com/sober235/DPP.