Deep learning methods have achieved attractive performance in dynamic MR cine imaging. However, most of these methods are driven only by the sparse prior of MR images, while the important low-rank (LR) prior of dynamic MR cine images is not explored, which may limit further improvements in dynamic MR reconstruction. In this paper, a learned singular value thresholding (Learned-SVT) operator is proposed to explore low-rank priors in dynamic MR imaging to obtain improved reconstruction results. In particular, we put forward a model-based unrolling sparse and low-rank network for dynamic MR imaging, dubbed as SLR-Net. SLR-Net is defined over a deep network flow graph, which is unrolled from the iterative procedures in the iterative shrinkage-thresholding algorithm (ISTA) for optimizing a sparse and LR-based dynamic MRI model. Experimental results on a single-coil scenario show that the proposed SLR-Net can further improve the state-of-the-art compressed sensing (CS) methods and sparsity-driven deep learning-based methods with strong robustness to different undersampling patterns, both qualitatively and quantitatively. Besides, SLR-Net has been extended to a multi-coil scenario, and achieved excellent reconstruction results compared with a sparsity-driven multi-coil deep learning-based method under a high acceleration. Prospective reconstruction results on an open real-time dataset further demonstrate the capability and flexibility of the proposed method on real-time scenarios.

Magnetic resonance (MR) image reconstruction from undersampled k-space data can be formulated as a minimization problem involving data consistency and image prior. Existing deep learning (DL)-based methods for MR reconstruction employ deep networks to exploit the prior information and integrate the prior knowledge into the reconstruction under the explicit constraint of data consistency, without considering the real distribution of the noise. In this work, we propose a new DL-based approach termed Learned DC that implicitly learns the data consistency with deep networks, corresponding to the actual probability distribution of system noise. The data consistency term and the prior knowledge are both embedded in the weights of the networks, which provides an utterly implicit manner of learning reconstruction model. We evaluated the proposed approach with highly undersampled dynamic data, including the dynamic cardiac cine data with up to 24-fold acceleration and dynamic rectum data with the acceleration factor equal to the number of phases. Experimental results demonstrate the superior performance of the Learned DC both quantitatively and qualitatively than the state-of-the-art.

Magnetic resonance imaging serves as an essential tool for clinical diagnosis. However, it suffers from a long acquisition time. The utilization of deep learning, especially the deep generative models, offers aggressive acceleration and better reconstruction in magnetic resonance imaging. Nevertheless, learning the data distribution as prior knowledge and reconstructing the image from limited data remains challenging. In this work, we propose a novel Hankel-k-space generative model (HKGM), which can generate samples from a training set of as little as one k-space. At the prior learning stage, we first construct a large Hankel matrix from k-space data, then extract multiple structured k-space patches from the Hankel matrix to capture the internal distribution among different patches. Extracting patches from a Hankel matrix enables the generative model to be learned from the redundant and low-rank data space. At the iterative reconstruction stage, the desired solution obeys the learned prior knowledge. The intermediate reconstruction solution is updated by taking it as the input of the generative model. The updated result is then alternatively operated by imposing low-rank penalty on its Hankel matrix and data consistency constraint on the measurement data. Experimental results confirmed that the internal statistics of patches within single k-space data carry enough information for learning a powerful generative model and providing state-of-the-art reconstruction.

Recently, low-dimensional manifold regularization has been recognized as a competitive method for accelerated cardiac MRI, due to its ability to capture temporal correlations. However, existing methods have not been performed with the nonlinear structure of an underlying manifold. In this paper, we propose a deep learning method in an unrolling manner for accelerated cardiac MRI on a low-dimensional manifold. Specifically, a fixed low-rank tensor (Riemannian) manifold is chosen to capture the strong temporal correlations of dynamic signals; the reconstruction problem is modeled as a CS-based optimization problem on this manifold. Following the manifold structure, a Riemannian gradient descent (RGD) method is adopted to solve this problem. Finally, the RGD algorithm is unrolled into a neural network, called Manifold-Net, on the manifold to avoid the long computation time and the challenging parameter selection. The experimental results at high accelerations demonstrate that the proposed method can obtain improved reconstruction compared with three conventional methods (k-t SLR, SToRM and k-t MLSD) and three state-of-the-art deep learning-based methods (DC-CNN, CRNN, and SLR-Net). To our knowledge, this work represents the first study to unroll the iterative optimization procedure into neural networks on manifolds. Moreover, the designed Manifold-Net provides a new mechanism for low-rank priors in dynamic MRI and should also prove useful for fast reconstruction in other dynamic imaging problems.

Diffusion models have emerged as a leading methodology for image generation and have proven successful in the realm of magnetic resonance imaging (MRI) reconstruction. However, existing reconstruction methods based on diffusion models are primarily formulated in the image domain, making the reconstruction quality susceptible to inaccuracies in coil sensitivity maps (CSMs). k -space interpolation methods can effectively address this issue but conventional diffusion models are not readily applicable in k -space interpolation. To overcome this challenge, we introduce a novel approach called SPIRiT-Diffusion, which is a diffusion model for k -space interpolation inspired by the iterative self-consistent SPIRiT method. Specifically, we utilize the iterative solver of the self-consistent term (i.e., k -space physical prior) in SPIRiT to formulate a novel stochastic differential equation (SDE) governing the diffusion process. Subsequently, k -space data can be interpolated by executing the diffusion process. This innovative approach highlights the optimization model’s role in designing the SDE in diffusion models, enabling the diffusion process to align closely with the physics inherent in the optimization model-a concept referred to as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method using a 3D joint intracranial and carotid vessel wall imaging dataset. The results convincingly demonstrate its superiority over image-domain reconstruction methods, achieving high reconstruction quality even at a substantial acceleration rate of 10. Our code are available at https://github.com/zhyjSIAT/SPIRiT-Diffusion.