MRI Reconstruction Method Based On Non-parametric Bayesian Dictionary Learning

With the progress of clinical medicine,magnetic resonance imaging(MRI)technology has been widely used in medical imaging because of its multiparameter imaging,arbitrary orientation fault,no harm to human body,high contrast of imaging.Therefore,the acquisition time of imaging data is required more fast.At present,the methods to solve this problem are mainly divided into two categories: the first is to make improvements in hardware,such as using multi-coil fast imaging;The other is to reduce the collection amount of K-space data.By the computer software,reconstruction is performed on the undersampling data,that is,the undersampling K-space reconstruction method.Undersampling K-space reconstruction does not need to increase the cost of hardware and is feasible,so it has been widely concerned by researchers.The development of compressed sensing(CS)theory and sparse representation theory provide a solid theoretical basis for undersampling K-space reconstruction.As an important part of CS theory,sparse representation and dictionary learning play important roles in improving the quality of MR image reconstruction.The existing dictionary learning methods are mainly divided into two parts: the analytic dictionary and adaptive learning dictionary.The analytic dictionary method is simple and efficient,but it can't match the best structure of image signal flexibly.The adaptive learning dictionary is based on the signal itself,so it has attracted much attention.However,adaptive learning image representation methods such as k-singular value decomposition(K-SVD)need to set the size of the dictionary,the sparsity of the signal and the regularization parameters in advance.These prior values need to be adapted to the image itself.If they are not set properly,it will directly affect the quality of dictionary learning.This thesis mainly focuses on how to train a dictionary with a more suitable way for the current image.We focus on sparse prior and dictionary learning to reconstruct MR images,the specific research contents are as follows:(1)MRI reconstruction model based on gradient domain and nonparametric Bayesian dictionary learning method is proposed.Firstly,the original MR image is transformed into the gradient domain,and then the dictionary is learned in the gradient domain image.In dictionary learning,nonparametric Bayesian dictionary learning method is introduced to replace the traditional K-SVD method.Considering that the lack of structure and clustering in the existing research results of nonparametric Bayesian dictionary learning method,this thesis,exploiting the stick-breaking construction of the beta process,proposes a nonparametric Bayesian dictionary learning method based on beta process.Because the proposed model is a multivariable coupling problem,ADM method and split Bergman method are used to decompose the NP hard problem into three sub-problems for solution.The Gibbs sampling method is used to update the dictionary learning variables so as to obtain a more suitable dictionary for the image signal itself.The experimental results show that: compared with several classical MRI reconstruction methods,the reconstruction quality of the proposed method is better,especially in the anti-noise performance.(2)In order to further improve the structural expression of dictionaries,considering the spatial position information of MR image,a nonparametric dictionary learning method using the Dirichlet-beta process is proposed and applied to the MRI reconstruction model mentioned above.In addition to using Gibbs sampling,we also use MAP(Maximum A Posteriori Estimation)method to infer the hidden variables.The experimental results show that: the peak signal-to-noise ratio of the proposed method is 0.84 d B higher than that of the above-mentioned reconstruction method,and the reconstruction quality is further improved.