Dynamic Magnetic Resonance Image Reconstruction Based On Sparse Sampling

Dynamic magnetic resonance imaging（DMRI）has been widely used in clinical area as an important medical imaging technology,and it is especially of vital importance in cardiac perfusion image and cardiac dynaminc imaging.In dynamic MRI such as cardiac MR imaging and MR perfusion imaging,which require a high real-time capability,traditional MRI can’t meet the requirements.How to reduce the data acquisition quantity,accelerate magnetic resonance imaging and obtain ideal spatial-temporal resolution have been the focus of dynamic MRI in recent years.To achieve the above aims,considerable efforts have been devoted to introducing compressed sensing（CS）theory into dynamic MRI,which make it possible that MR image can be reconstructed from k-space data at relative a low sampling rate.This dissertation discusses dynamic MR image reconstruction based on compressed sensing.The main contents of this dissertation are as follows:（1）A reconstruction method using L₀ total variation（TV）minimization is proposed.MR images are highly sparse in finite difference domain.This method constrains L₀ norm of image gradient instead of L₁ norm to promote the sparsity of signals in gradient domain where L₀ gradient is defined as the number of the non-zero gradient of the image,which constrains the optimization problem.Through the above method,we can achieve a more precise image.According to CS theory,L₀ norm minimization requires less measurements than L₁ norm,which accelerate the magnetic resonance imaging.The object function is decomposed by Alternating Direction Method of Multipliers（ADMM）into several sub-problems which are solved iteratively to reconstruct the MR image.The simulation results demonstrate that the proposed method can constrain the sparsity of images,obtain better reconstruction quality than traditional method at same sampling rate and reduce relative error effectively.（2）A fast reconstruction method with ADMM based on difference in spatial and temporal domain is proposed.Exploiting the sparsity of MR image in spatial and temporal difference domain,this method utilizes the L₁ norm of three dimensional TV of dynamic MR image as a regularization term to penalize the reconstruction model.The reconstruction problem is solved by ADMM to achieve a fast dynamic MR image reconstruction.On the above basis,we replace the original Conjugate Gradient（CG）method in k-t SLR method with our fast method which utilizes dot products of matrices in order to improve the original k-t SLR method.Several experimental results demonstrate that the improved k-t SLR method can reduce the operating time to 10%of the original operating time,which accelerate the imaging proceeding to a great extent.