Dynamic MRI Reconstruction Algorithm Based On Low Rank Constraint

Dynamic magnetic resonance imaging is an important imaging technology in medicine.Because of its high contrast and no ionizing radiation,dynamic magnetic resonance imaging is widely used in a variety of medical detection scenes.Due to the limitations of the physical level,signal acquisition takes a long time in the process of magnetic resonance imaging,coupled with the fact that the human body is prone to involuntary movement,the spatio-temporal resolution of imaging is not high,so the clinical application of dynamic magnetic resonance imaging is limited.Therefore,the reduction of the scanning time and promotion of the imaging speed are the important research directions in the field of magnetic resonance imaging.Compressed sensing can make use of the sparse characteristics of magnetic resonance images to sample in a way that is much less than the sampling rate of Nyquist.Combined with correlation optimization algorithm,the imaging speed is greatly improved.The theory of low-rank matrix recovery makes compressed sensing break away from the limitation of vector space and can complete the missing part of low-rank matrix.The high temporal correlation of dynamic magnetic resonance sequence is used to realize dynamic magnetic resonance image reconstruction.Exploring the method of efficiently using the low rank of image sequences is the key to the research of dynamic magnetic resonance image reconstruction based on low rank constraints.This paper focuses on the image reconstruction model based on low-rank plus sparse decomposition,low-rank plus second-order generalized total variational constraints and local low-rank sparse constraints.The key research work includes:First of all,for the low-rank plus sparse model,the quadratic term updating is complex and the computational efficiency is low when the variable splitting method is used to solve the convex optimization problem.In this paper,under the augmented Lagrangian framework,an efficient variable splitting method in the form of collection operator is proposed,which can avoid complex conjugate iterations and reduce the computing time of the algorithm.The experimental results show that for dynamic magnetic resonance reconstruction,the proposed method can obtain good image quality and has faster reconstruction speed than iterative soft threshold algorithm and conjugate gradient method.Secondly,the generalized total variation is used instead of the l₁ norm for sparse constraints.The temporal coherent background is represented by kernel norm,and the sparse dynamic components are represented by spatio-temporal generalized total variational functional.A new decomposition model based on generalized total variation and kernel norm is proposed,which is solved by first-order primal-dual algorithm.The model is compared with the existing methods on different data sets and different sampling factors.The experimental results show that this method can not only obtain high signal error ratio and structural similarity,but also suppress spatial artifacts and preserve edges.Finally,aiming at the problem of global low-rank possible fuzzy space details and local low-rank sensitivity to block size,an adaptive local low-rank sparse constraint model is proposed.The spatial details are smoothed by adaptively adjusting local block size and low-rank regularization parameters,and solved by fast iterative soft threshold method.The experimental results show that this method improves the peak signal-to-noise ratio and visual information fidelity,fully suppresses fringe artifacts,and has higher transition sharpness,and the greater the acceleration factor R,the more obvious the improvement.