Nuclear Norm Minimization Improved Algorithms For Dynamic Magnetic Resonance Image Reconstruction

Dynamic Magnetic Resonance Imaging(dMRI) is an important biomedical study and diagnostic technology. However, the scan time of magnetic resonance imaging was so long that the patient cannot understand and produce involuntary movement which had a serious impact of the reconstructed medical image quality. In order to reduce the imaging time in clinical application, the physical methods that through improve the intensity of main magnetic and gradient field have reached the end, so it must use certain mathematical methods to improve reconstruction speed. Therefore, it is more urgent on how to get clear images through fast reconstruction in the magnetic resonance imaging. this paper mainly aims at in-depth research on dynamic MR imaging algorithm and improved algorithm.In this paper, low-rank representation is introduced in dynamic magnetic resonance image reconstruction process, using each temporal frame as a column of a space-time matrix, where the spatio-temporal correlations produce a low-rank matrix. The low-rank matrix is solved by nuclear-norm minimization. This paper in view of the large-scale image sequence data, it is focused on the improved algorithms of nuclear-norm minimization in the framework of alternating direction method, and depth research on the first-order methods of dynamic magnetic resonance image reconstruction.Nuclear norm minimization iterative algorithm involves the singular value decomposition(SVD).To reduce the complexity, we used low-rank matrix separation instead of SVD. Firstly, the data matrix is separated to two low-rank matrix products. Then, constraints are converted to augmented Lagrangian function to solve each block minimization problem. The algorithm avoids SVD of each iteration and reduces the complexity. New method has good effect on the matrix completion, the computing time is greatly optimized and the relative error is reduced, so the efficiency of the algorithm was improved.In this paper, we study the dynamic magnetic resonance image reconstruction for the two models, dynamic MRI via nuclear norm minimization and an accelerated proximal gradient, and dynamic MRI via low-rank plus sparse decomposition reconstruction. The objective function of the first model contains data fitting items and nuclear norm, the method is based on nuclear norm minimization and an accelerated proximal gradient algorithm, by solving the nuclear norm regularized linear least squares problem to complete the image reconstruction. In the experiment of PINCAT data and real cardiac MRI data, the improved algorithm under this model has a better effect for image reconstruction.The objective function of the second model contains data fitting items, nuclear norm and 1l norm, the algorithm is based on a low-rank plus sparse decomposition prior, by regularizing the inverse problem based on an alternating direction method to complete the image reconstruction. In the experiment of phantom simulated data and real cardiac MRI data, the improved algorithm under the model also has a better effect for image reconstruction.