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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]

Background: Wave gradient encoding can adequately utilize coil sensitivity profiles to facilitate higher accelerations in parallel magnetic resonance imaging (pMRI). However, there are limitations in mainstream pMRI and a few deep learning (DL) methods for recovering missing data under wave encoding framework: the former is prone to introduce errors from the auto‐calibration signals (ACS) signal acquisition and is time‐consuming, while the latter requires a large amount of training data. Purpose: To tackle the above issues, an untrained neural network (UNN) model incorporating wave‐encoded physical properties and deep generative model, named WDGM, was proposed with additional ACS‐ and training data‐free. Methods: Generally, the proposed method can provide powerful missing data interpolation capability using the wave physical encoding framework and designed UNN to characterize the MR image (k‐space data) priors. Specifically, the MRI reconstruction combining physical wave encoding and elaborate UNN is modeled as a generalized minimization problem. The designation of UNN is driven by the coil sensitivity maps (CSM) smoothness and k‐space linear predictability. And then, the iterative paradigm to recover the full k‐space signal is determined by the projected gradient descent, and the complex computation is unrolled to the network with optimized parameters by the optimizer. Simulated wave encoding and in vivo experiments are exploited to demonstrate the feasibility of the proposed method. The best quantitative metrics RMSE/SSIM/PSNR of 0.0413, 0.9514, and 37.4862 gave competitive results in all experiments with at least six‐fold acceleration, respectively. Results: In vivo experiments of human brains and knees showed that the proposed method can achieve comparable reconstruction quality and even has superiority relative to the comparison, especially at a high resolution of 0.67 mm and fewer ACS. In addition, the proposed method has a higher computational efficiency achieving a computation time of 9.6 s/per slice. Conclusions: The model proposed in this work addresses two limitations of MRI reconstruction in the wave encoding framework. The first is to eliminate the need for ACS signal acquisition to perform the time‐consuming calibration process and to avoid errors such as motion during the acquisition procedure. Furthermore, the proposed method has clinical application friendly without the need to prepare large training datasets, which is difficult in the clinical. All results of the proposed method demonstrate more confidence in both quantitative and qualitative metrics. In addition, the proposed method can achieve higher computational efficiency. [ABSTRACT FROM AUTHOR]

Recently, untrained neural networks (UNNs) have shown satisfactory performances for MR image reconstruction on random sampling trajectories without using additional full-sampled training data. However, the existing UNN-based approaches lack the modeling of physical priors, resulting in poor performance in some common scenarios (e.g., partial Fourier (PF), regular sampling, etc.) and the lack of theoretical guarantees for reconstruction accuracy. To bridge this gap, we propose a safeguarded k -space interpolation method for MRI using a specially designed UNN with a tripled architecture driven by three physical priors of the MR images (or k -space data), including transform sparsity, coil sensitivity smoothness, and phase smoothness. We also prove that the proposed method guarantees tight bounds for interpolated k -space data accuracy. Finally, ablation experiments show that the proposed method can characterize the physical priors of MR images well. Additionally, experiments show that the proposed method consistently outperforms traditional parallel imaging methods and existing UNNs, and is even competitive against supervised-trained deep learning methods in PF and regular undersampling reconstruction. • A physical prior-driven untrained neural network was proposed for MRI reconstruction. • The accuracy of the proposed model's MRI reconstruction was analyzed. • Experimental results confirmed model's superiority in MRI reconstruction. [ABSTRACT FROM AUTHOR]