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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. [ABSTRACT FROM AUTHOR]

Background: Deep learning methods driven by the low‐rank regularization have achieved attractive performance in dynamic magnetic resonance (MR) imaging. The effectiveness of existing methods lies mainly in their ability to capture interframe relationships using network modules, which are lack interpretability. Purpose: This study aims to design an interpretable methodology for modeling interframe relationships using convolutiona networks, namely Annihilation‐Net and use it for accelerating dynamic MRI. Methods: Based on the equivalence between Hankel matrix product and convolution, we utilize convolutional networks to learn the null space transform for characterizing low‐rankness. We employ low‐rankness to represent interframe correlations in dynamic MR imaging, while combining with sparse constraints in the compressed sensing framework. The corresponding optimization problem is solved in an iterative form with the semi‐quadratic splitting method (HQS). The iterative steps are unrolled into a network, dubbed Annihilation‐Net. All the regularization parameters and null space transforms are set as learnable in the Annihilation‐Net. Results: Experiments on the cardiac cine dataset show that the proposed model outperforms other competing methods both quantitatively and qualitatively. The training set and test set have 800 and 118 images, respectively. Conclusions: The proposed Annihilation‐Net improves the reconstruction quality of accelerated dynamic MRI with better interpretability. [ABSTRACT FROM AUTHOR]