Generalized Structured Low-rank Matrix Recovery And Application In Magnetic Resonance Image Reconstruction

Magnetic Resonance Imaging(Magnetic Resonance Imaging,MRI)has become one of the most advanced imaging techniques in conventional medical diagnosis and medical imaging because of its many advantages such as no radiation hazard,high imaging contrast,and multi-angle imaging of various organs of the human body..At the same time,dynamic magnetic resonance imaging can show blood movements of the brain and heart movements.With the continuous development and optimization of dynamic magnetic resonance imaging,perfusion imaging technology has gradually become a new and effective medical method.But whether it is two-dimensional or dynamic magnetic resonance imaging technology,the slow imaging speed has always been one of the factors restricting the efficiency of magnetic resonance imaging and the quality of imaging.Sampling is performed in a way that is much smaller than the Nyquist sampling rate,and reducing the number of samples to increase sampling and imaging speed is one of the ideas to solve this problem.The article starts with the convolutional zeroing relationship in the frequency domain of the piecewise smooth one-dimensional signal,and converts the signal convolution process to the multiplication process of the structured matrix,and the structured matrix constructed can prove to be low rank.Similar to the one-dimensional signal,the two-dimensional signal has a similar convolutional zeroing relationship,that is,a structured low-rank matrix can be constructed.The low-rank nature of the structured matrix can be used to construct an optimization model to reconstruct the matrix with missing information.This is the principle of structured low-rank matrix recovery and is also the theoretical basis of this research.Based on this theory,this article will study the generalized structured low-rank matrix recovery and its application in magnetic resonance imaging.This paper first studies 2-dimensional MR images reconstruction algorithm based on generalized structured low rank matrix(GSLR),using the structure constructed by k-space data The rank of the matrix is used as a constraint to construct an optimization model.Because the size of the matrix is large,this paper will use the alternating direction multiplier method(ADMM)which can save computing costs and speed up convergence to iterate the optimization problem.At the same time,the magnetic resonance image is converted into the sum of the block constant part and the block linear part.The two parts of the sampled data are used to construct a structured low rank matrix,which is a generalized structured low Rank matrix.The simulation results are discussed in terms of reconstruction quality and execution time.Secondly,the algorithm is expanded.In the process of constructing the structured matrix,not only the image spatial domain information is used,but also the correlation between frames of the dynamic image sequence is added.Extend the application scenarios of the algorithm from 2-dimensional images to dynamics,study the dynamic MR image reconstruction algorithm based on generalized structured low-rank matrix(GSLR),and analyze and discuss the performance of the algorithm in terms of the quality and time cost of reconstructed images.Dictionary learning is one of the hotspots of current research.This is a method of sparsely encoding images based on their sparsity to obtain sparse representations.Therefore,the idea of analyzing dictionary learning is combined with the generalized structured low-rank matrix theory studied in this article.The pre-trained adaptive dictionary is used as a weight to sum the weighted structured matrix constructed by different operators,and the iterative optimization method is used to solve the optimization.problem.Finally,this paper studies the MR image reconstruction based on the GSLR a priori deep learning method.Under the background of deep learning,the traditional regularization method can be summarized as a deep network with repeated convolution and deconvolution,and its structure is very similar to the convolutional neural network(CNN).Therefore,considering the method of deep learning,combined with the prior knowledge of the generalized structured low rank matrix,a deep learning network based on GSLR prior is proposed,and the network performance is analyzed and discussed based on the simulation results.