The Research On MR Imaging Reconstruction By Using Tight Frame Based Sparse Representation And Nonconvex Low-Rank

Magnetic resonance imaging(MRI)has the advantages of no ionizing radiation,multi-angle imaging,and no damage to human tissues,and thus has become a very important detection method in clinical diagnosis and medical research.However,the shortcomings of MRI are slow imaging speed and low dynamic MRI time resolution.At the same time,scan time for the patient is too long and the cost is too high,which limits the further promotion of MRI.Compressed Sensing(CS)theory breaks through Nyquist's sampling law,which utilizes the compressibility and sparsity to reconstruct images without aliasing from very few observations.Magnetic resonance imaging based Compressed Sensing(CS-MRI)technology has become the focus of rapid magnetic resonance imaging research.In this paper,we focus on the two kinds of prior knowledge of image sparse representation and low rank constraint in compressed sensing theory to reconstruct magnetic resonance images.The specific research contents are as follows:(1)In this paper,sparse representation of tensor product complex tight framelets(TPCTF)based sparse representation is proposed to implement MR image reconstruction.Although the traditional wavelet function can be used to sparsely represent signals,the ability to characterize the image is insufficient,and the signal decomposition cannot be sufficiently sparse.As a tight framelets,TPCTF provides ideal characteristics for multi-directional selectivity and translation invariance.These features provide a sparse directional representation of natural images,which can capture image edges and texture information very well.Moreover,the projected fast iterative soft threshold algorithm(pFISTA)is introduced to perform the TPCTF based MR image reconstruction,which can not only achieve the accuracy of the alternating direction multiplier method(ADMM)algorithm,but also has a faster convergence speed.In order to adaptively shrink the wavelet decomposition coefficients,we also use the bivariate shrinkage function is also proposed for threshold processing.The experimental results show that,when compared with other the state-of-the-art CS-MRI algorithms in numerical experiments,the proposed TPCTF-BS method can not only achieve a higher reconstruction quality,but also a faster reconstruction speed.(2)In this paper,the weighted Schatten p-norm minimization(WSNM)method is proposed to implement magnetic resonance imaging reconstruction,acted as low rank constrains.The nonlocal self-similarity of magnetic resonance images,the nonconvex Schatten p-norm and the weighting factors of the importance of different rank elements are integrated together as the low rank constraint to regularize the MRI reconstruction.In addition,the Alternating Direction Method of Multipliers(ADMM)algorithm is used to solve the non-convex minimization problem of MRI reconstruction based WSNM.Compared with other state-of-the-art methods in numerical experiments,the proposed method achieves a higher reconstruction quality with higher peak signal to noise ratio(PSNR)and better structural similarity(SSIM)index.