| Magnetic Resonance Imaging(MRI)has become an important medical Imaging technology due to its advantages,such as no ionizing radiation,non-invasive and high soft-tissue contrast.However,the raw data of magnetic resonance is acquired sequen-tially in k-space,and the traversal speed of K space is limited by physiology and hardware,resulting in a very slow data collection.The long data acquisition not only leads to motion artifacts caused by a slight movement of the scanned object,but also increases the cost of imaging and the difficulty of acquisition.At present,k-space undersampling to accelerate scan is an important strategy for rapid MRI imagingDynamic magnetic resonance imaging(dMRI)is of great value in clinical appli-cations,such as cardiac imaging,interventional therapy,vocal tract detection,cancer evaluation,and other clinical applications,due to its ability to reveal spatial anatomical information and dynamic information simultaneously.However,the tradeoff between Spatio-temporal resolution,spatial coverage,and signal-to-noise ratio of dMRI makes accelerated dMRI one of the most challenging MRI techniques.In the past decades,Parallel Imaging(PI),Compressed Sensing(CS),Low Rank(LR)matrix completion,Manifold Learning(ML),and other methods have made great progress in solving this challenge.These methods use the spatial position prior,sparse prior,and low-rank prior of dynamic signals to build a reconstruction model,and solve the constructed model through an optimization algorithm,to get the reconstructed MR image.However,the limitations of these methods,such as limited acceleration ratio,tedious adjustment of hyperparameters,and long solution time,hinder their clinical applicationRecently,deep learning(DL)methods have achieved some success in accelerated dMRI,promising to address these limitations.These DL methods use a large number of fully sampled data to train neural networks to learn the mapping relationship from undersampled images to fully sampled images.In the test stage,undersampled images is input into the trained neural network,and the neural network can output the recon-structed image.Nevertheless,there is still room for improvement in the reconstruction performance of DL methods in dMRI.Firstly,the current DL methods only extract features in the image domain and do not make full use of the frequency domain features of the k-space data.Secondly,these methods are driven only by the sparse prior of MR images,while the important low-rank(LR)prior of dynamic MR images is not explored Thirdly,the current manifold learning methods only regard the manifold hypothesis as a regularization constraint,and their optimal trajectories in Euclidean space do not fit the nonlinear manifold structure.Fourthly,DL methods rely on high-quality dynamic data,but the acquisition of dMRI data is very difficult and requires a lot of manpower and material resources.Focusing on the key technical problems of accelerated dMRI and aiming at the above limitations,this paper studies the dMRI technologies based on deep learning.The main research work and achievements are as follows:·Sparsity Driven:A cross-domain multi-supervised convolutional neural network has been proposed to extract frequency domain and image domain featuresAlthough DL methods can effectively alleviate the limitations of the traditional iterative methods,such as slow reconstruction speed and difficult parameter adjustment,they all construct the entire network in the image domain.They do not make full use of the information in the frequency domain.In this paper,a cross-domain(frequency/spa-tial domain)learning model is built based on a cascaded convolutional neural network Through the alternation of the frequency domain network and spatial domain network,this cross-domain model can simultaneously learn the characteristics of frequency do-main and spatial domain.The frequency-domain network is used to predict the k-space of full acquisition,and the spatial-domain network is used to extract the image features The two networks are connected by inverse Fourier transform.The frequency-domain network and the spatial-domain network use the data consistency layer to correct the k-space data.Moreover,a technique of multi-supervised loss function is introduced to restrict the reconstruction results at different stages to ensure that the reconstruction results of different network depths are as close as possible to the full image acquisi-tion.Compared with the state-of-the-art CS and DL methods,the proposed method can obtain higher quality reconstruction results·Low-rank Driven:A neural network based on sparse and low-rank priors has been designed to incorporate low-rank prior into deep learning methodsThe low rank prior of dynamic MR images has been well verified in the traditional optimization methods.However,the current DL-dMRI acceleration methods only uti-lize the sparse prior of the signal.The low-rank prior of the dynamic signal has not been explored in any DL-dMRI methods.In this paper,a novel convolutional neural network based on deep low rank prior is proposed.Specifically,the reconstruction of MR cardiac image is modeled as a multi-constraint optimization problem,which consists of data consistency constraint,sparse constraint,and low-rank constraint.The ISTA algorithm is used to solve the optimization problem,and the iterative procedures are obtained.Then,we unroll the iterative procedures into a neural network and use the neural network to learn the hyperparameters and transformations in the optimization problem.Finally,we obtain the neural network,SLR-Net,based on the sparse and low-rank model.A large number of experiments(single/multi-coil,retrospective/prospective reconstruction,different sampling patterns)have demonstrated that SLR-Net can sig-nificantly improve the quality of dMRI reconstruction.To our knowledge,this work represents the first study applying a learned low-rank prior to dynamic MR images,and it is expected to be extended to other dynamic applications.·Manifold Driven:A deep manifold neural network,which introduces the Rie-mannian optimization on the manifold into a deep learning methodManifold learning assumes that dynamic MR images are neighboring points on a low-dimensional smooth manifold and embeds this assumption as a regularization term in a compressed sensing framework.The correlation between image frames is characterized by the manifold nonlinear topology.However,the existing manifold regularization methods are solved in linear Euclide space.The optimized trajectory does not fit the nonlinear topology structure of the manifold,which easily leads to problems such as slow convergence and large reconstruction error.In this paper,a novel deep manifold neural network is proposed.Specifically,we design a fixed rank manifold and build an optimization model on it.Then,a Riemannian optimization technique is used to solve the optimization problem on the manifold.The solving process includes gradient calculation,tangent space projection,and retraction to the manifold.Then,we unroll the Manifold optimization process into a neural network,using the neural network to learn the hyper-parameters and transformations,and obtain the Manifold network,Manifold-Net.Compared with the traditional compressed sensing methods and the state-of-the-art deep learning methods,Manifold-Net achieves high-quality reconstruction under 12-fold acceleration.This work represents the first study unrolling the optimization on manifolds into neural networks.Besides,the designed low-rank manifold provides a new technical route for applying low-rank priors in dynamic MR imaging.·Unsupervised Driven:An unsupervised learning technology based on time-interleaved sampling strategy avoids the collection of fully sampled dataDL-dMRI methods require a large number of high-quality images as the ground truth to train the network model.However,the establishment of the dMRI database is very difficult and expensive.In addition,most CMR deep learning reconstruction studies utilize simulated single-channel k-space data to train the network,which leads to the underutilization of coil correlation.In this work,we propose an unsupervised deep learning method via a time-interleaved sampling strategy.Specifically,a time-interleaved acquisition scheme is utilized to build a set of fully encoded reference data by directly merging the k-space data of adjacent time frames.Then these fully encoded data can be used to train a parallel network for reconstructing images of each coil separately.Finally,the images from each coil are combined via a CNN to implicitly explore the correlations between coils.The comparisons with the state-of-the-art methods on in vivo datasets show that our method can achieve improved reconstruction results in an extremely short amount of time.The research works in this paper promote the theoretical perfection and application of dynamic MR imaging:The cross-domain information is used effectively,and the multi-supervision technology improves the reconstruction results at all levels;Low-rank prior is introduced into a deep-learning-based method for dynamic MR imaging;Riemannian optimization on manifolds is combined with a deep learning method for the first time;The feasibility of the unsupervised learning technique for dynamic MR imaging is explored. |
