Research On Sparse Reconstruction Method For Magnetic Resonance Imaging

As an important imaging technology nowadays,magnetic resonance imaging has the characteristics of detailed imaging,non-invasive and non-ionizing imaging,which has been widely used in clinical diagnostic medicine and related imaging science.However,relatively slow imaging speed still restricts the development of this technology.Compressed sensing theory can accurately reconstruct magnetic resonance images with a small amount of incoherent sampling data and appropriate optimization algorithms.Thus,on the basis of compressed sensing theory,this thesis focuses on the sparse representation and reconstruction algorithms for magnetic resonance imaging,and proposes three improved sparse reconstrcution methods to achieve the accurate reconstruction of magnetic resonance images.The main research content is as follows.Firstly,the second-order total generalized variation model is used to replace the traditional total variation model,and an adaptive reconstruction method is proposed based on the second-order total generalized variation model.This method uses the fitting characteristics of the high-order term in total generalized variation model to balance the reconstruction penalties of different structural regions in the image,and improves the selection of weight coefficients so as to be modified adaptively during the iterative process of solving the objective function.Compared with the traditional fixed total variation model,this method has obvious advantages in preserving the image geometry structure and edge features,and can effectively reduce the residual value of reconstruction results in simulation experiments with serveral measurement rate,and the peak signal to noise ratio increases about 2.90 dB on average under 20% measurement rate.Secondly,analyzing the nonlocal similarity of the magnetic resonance images and sparse characteristics of the low-rank matrix constructed by similar image patches,an improved reconstruction method based on dynamic singular value shrinkage of low-rank matrix is proposed.This method firstly performs similar image patches matching and constructs a low-rank matrix dictionary to build an objective function,and then uses the dynamic singular value shrinkage method to solve the low-rank constraint problem.Besides,the alternating direction multiplier method is applied in the iterative calculation of objective function.Simulation results show that this method has better image texture preserving ability and higher reconstruction quality in multi-tissue reconstruction experiments,and the peak signal to noise ratio increases about 2.47 dB on average under 20% measurement rate.Finally,aiming at the deficiency of the single sparse constrained model and then fully exploiting images' features in different sparse representation domains,a reconstruction method based on multi-regularization constraints is proposed.This method firstly constructs the multi-regularization objective function,which takes the advantage of the total generalized variation model's high-order smoothing property and the low-rank constraint model's preserving property.Then,the split Bregman iteration algorithm is used to solve the objective function,which splits the whole function into several sub-problems.Simulation results show that the proposed method has better reconstruction quality than other typical multi-regularization constraint methods.The peak signal to noise ratio respectively increase about 2.82 dB and 3.58 dB on average under 20% measurement rate in the multi-tissue imaging experiments and the multi-parameter imaging experiments.This thesis works on the research of exploiting the global sparse representation and the self-structured features for magnetic resonance images,and several improved reconstruction methods are proposed.These methods are simulated and verified in multigroup experiments,and also provide new solutions to sparse reconstruction for magnetic resonance images.