Low Rank Tensor Reconstruction For Fast Magnetic Resonance Image

Magnetic resonance imaging(MRI)has been wildly used in field of clinical diagnosis,including dynamic Magnetic resonance imaging(DMRI)for long-term observation of an organ and Magnetic resonance fingerprinting(MRF)for quantitative imaging,but it suffers from the slow imaging speed and low efficiency.For acceleration,how to improve the quality of reconstruction from a limited set of under-samples is a crucial problem.Compressed sensing,on the premise of keeping the observation matrix and sparse matrix incoherent,recovers high-quality image by collecting part of the signal information to solve the optimization model,which breaks the restriction of Nyquist sampling theorem that the sampling rate must be greater than twice the signal frequency,and greatly reduces the amount of signal sampling.Moreover,the method based on tensor can further improve the restoration effect of MRI image by using temporal and spatial correlation.The focus of the article is exploring the improvement of DMRI and MRF image recontruction algorithm based on compressed sensing:(1)Smooth tensor robust principal component analysis for DMRI reconstruction.The low-rank plus sparse decomposition model,which is also called robust principal component analysis(RPCA),is widely used for reconstruction of DMRI in an unsupervised way.Considering that DMRI data is naturally in tensor form with block-wise smoothness,we propose a smooth robust tensor principal component analysis method(SRTPCA)for the dynamic magnetic resonance image reconstruction.Compared with classical RPCA ways,the low rank and sparsity terms are extended to tensor space to fully exploit the spatial and temporal data structures.Moreover,a tensor total variation regularization term is used to encourage the multi-dimensional blockwise smoothness for the reconstructed dynamic MRI data.The relaxed convex optimization model can be divided into several sub-problems by the alternating direction method of multipliers algorithm.Numerical experiments on cardiac perfusion and cine datasets demonstrate that the proposed SRTPCA method exceeds the state-of-the-art ones in recovery accuracy.(2)Tensor low rank model for MRF reconstruction.In view of the difference between MRF and DMRI in imaging methods,processing steps and imaging purposes,and the evolution of MRF signal must be included in the dictionary,and signal evoluaiton in single voxel can be represented by one atom of dictionary at most,as well as the spatio-temporal correlation of MRF signal,we propose a method based on low tensor and subspace,using tSVD,CP and Tucker decomposition.The incremental projection gradient descent method based on temporal projection is used to tackle the problem,and the Nesterov method is used to accelerate the convergence.Compared with the matrix based method,the matched organization parameter map has a significant improvement,and the NRMSE measurement of the error with the ground truth also shows its effectiveness.