First-order Method For TV Image Reconstruction With Application To Partially Parallel Mr Imaging

Parallel magnetic resonance imaging plays an important role in medical imaging. In Parallel magnetic resonance imaging, multiple receiver coil arrays are used to collect data at the same time, while maintaining spatial resolution is not in the case of attenuation. It can decrease sub-sample K-space data to reduce the magnetic resonance imaging scanning time and improve imaging speed. Total variational image reconstruction is one of the current research focuses for parallel magnetic resonance imaging. And the edge information of Total variational image reconstruction is better than L1 image reconstruction. The first-order methods are wildly used in total variational image reconstruction. They are only involves the objective function values and gradient information in the process of iteration, especially suitable for the large scale problems. However, how to effectively use the first-order methods to realize automatic real-time fast high quality of parallel magnetic resonance imaging is still extremely important and unsolved problem.In view of the best uniform rate of convergence for first-order methods depends very strongly on smoothness, where the inversion matrix is large and ill-conditioned, the paper has researched and discussed these problems. In this process, the main innovation is reflected in the following aspects:Douglas-Rachford splitting algorithm based on parallel magnetic resonance imaging is given. In view of the limitation that incomplete undersampling data of the traditional Sensitivity encoding(SENSE) lead to ill-conditioned matrix, the paper utilizes variable splitting techniques to reduce the imageing reconstruction problem to a constrained minimization problem and improve the objective function of SENSE. The new algorithm takes the advantage of Douglas-Rachford splitting algorithm, and makes use of the spatial neighborhood information, and improves the quality of the image restoration, and has better convergence.An adaptive alternating direction multiplier method based on particlly parallel imagingis given. In view of the limitation that fixed stepsize of alternating direction multiplier method, the paper combines the traditional alternating direction multiplier method and Barzilai-Borwein method to deal with non-convex total variation regularization. The new algorithm not only has obtained better segmentation effet, but also has better convergence and stability.An adaptive Primal-Dual hybrid gradient method based on total variation image restoration is given. In view of Primal-Dual hybrid gradient methods require the user to choose stepsize parameters, the paper introduce new adaptive Primal-Dual hybrid gradient method that automatically tunes the stepsize parameters for fast convergence without user inputs. The paper combines the concept of residual balancing to automatically tune the stepsize parameters and and obtain better convergence speed. Experiments show that the effect of new algorithm for image restoration is better, to a certain extent solved the convergence problem of Primal-Dual hybrid gradient method.