MRI Reconstruction Method Based On Anisotropic Total Variation Regularization

Magnetic Resonance Imaging(MRI)is a kind of imaging technology,which uses the signal generated by nuclear resonance in the magnetic field to reconstruct the image.As a new medical imaging diagnostic method,because of the advantages of abundant diagnostic information and no ionizing radiation,it has played an important role in medical imaging research.However,due to the factors of MRI instrument itself,the image signal directly acquired is easily corrupted by noise and acquisition methods,In order to recover highquality image from degraded image,researchers have proposed many variational models,such as total variation(TV),weighted total variation(WTV),directional total variation(DTV).In the process of image reconstruction,although the total variation model can effectively maintain edges,it often leads to staircase artifacts.Therefore,how to effectively maintain the structural information of the image is an important research orientation in the MRI reconstruction problem.During MRI scanning,although T1 and T2 weighted image are quite different,their edge structures have a high correlation because they are the same anatomical structure.In order to improve the image quality,T1 and T2 weighted image are combined for reconstruction.That is,the edge position information in one contrast is incorporated into the reconstruction of another image.It has received extensive attention in recent years.Among the established models,the DTV model has an important influence.To this end,this dissertation makes the following research based on the DTV model:· This dissertation proposes a robust numerical solution method based on the DTV model.Since the DTV model is a non-smooth convex optimization problem coupled multiple linear operators,the unconstrained minimization problem is transformed into an equality constraint problem by introducing auxiliary variables.Then we use the alternating direction multiplier method(ADMM)to solve each subproblem.It not only reduces the complexity of the calculation,but also speeds up the convergence.· In order to reconstruct MRI image more effectively,this dissertation improves the regularization term of the model on the basis of the directional total variation model.Specifically,a robust total variation image reconstruction model(DTVP)is proposed based on the non-convex ?p-quasi module term as the regularization term.Since the pro-posed model is non-convex and non-lipschitz,we use the alternating direction multiplier method to convert it into multiple subproblems that can be easily solved.Especially for the l~2-l~p psubproblem,we use the alternating direction method to solve it under the semi-quadratic type.The results of numerical experiments show that the proposed model can effectively reconstruct magnetic resonance image.