Research On MR Image Reconstruction Based On Tensor Low Rank Sparse Decomposition

Dynamic magnetic resonance imaging enables high-contrast imaging of spatial stereoscopic or dynamically changing parts without radioactive hazards,such as ionizing radiation.The range of its application is wider than that of general static magnetic resonance imaging.However,further developments are constrained by slow data acquisition and imaging speed.With the development and improvement of compression sensing theory,magnetic resonance image reconstruction based on compressed sensing has become a research focus.Most of the existing compressed sensing MRI methods generally convert 3D or higher-dimensional magnetic resonance image data into a two-dimensional space for processing.Obviously,resetting high-dimensional data to a two-dimensional matrix will destroy the logical relationship between the data,and ignore its intrinsic correlation,thus affecting the quality of high-dimensional magnetic resonance image reconstruction.Tensor can represent high-dimensional data naturally,and tensor decomposition technique has been widely used in multi-dimensional signal processing,and has achieved good performances.Therefore,in this paper the low rank sparse-based tensor decomposition method is proposed to improve the reconstructed image quality and speed up image reconstruction.The specific research in this paper is as follows:(1)An improved robust tensor principal component analysis method is proposed to implement dynamic MR image reconstruction.Robust tensor principal component analysis can effectively capture the structural information of multidimensional data,and is widely used in multi-dimensional signal processing,such as background modeling,subspace clustering,and video compression.Therefore,the high-dimensional magnetic resonance image reconstruction problem is decomposed into two sub-part recovery problems with low rank tensor and sparse tensor based on robust principal component partitioning mechanism,constrains are added to low rank tensor and sparse tensor at the same time.This paper introduces a new tensor nuclear norm,and solves the problem of low-rank tensor constraint deficiency by adding matrix nuclear norm;adding the l1 norm constraint after Fourier transform of sparse tensor;finally using iterative soft threshold shrinkage algorithm to solve the optimization problem.The experimental results show that the proposed improved robust tensor principal component analysis method performs better in reconstructing dynamic MR image than the two-dimensional matrix and general three-dimensional compressed sensing magnetic resonance image reconstruction methods.This method can not only achieve good reconstruction quality,but also greatly improves the reconstruction speed.(2)An adaptive sequentially truncated high-order singular value decomposition method is proposed to perform dynamic MR image reconstruction.Firstly,the high-dimensional magnetic resonance image reconstruction problem is transformed into low-rank plus sparse tensor recovery problem.The adaptive sequentially truncated high-order singular value decomposition method is used to approximate the low-rank tensor.And the sparse tensor is sparsely transformed by using Fourier transformation,and the l1 norm constraint is added.In addition,the iterative soft threshold algorithm is used to solve the minimization problem.Through the 3D experiment,it is proved that the method proposed in this chapter can improve the reconstructed image quality and reduce the image reconstruction time.Through 4D experiments,the method is proved effectively in high-dimensional magnetic resonance imaging applications.