Research On Magnetic Resonance Image Reconstruction Based On Low-rank Constraint

Magnetic Resonance Imaging(MRI)has been a conventional method in medical diagnosis and one of the most advanced technology in medical imaging due to its advantage of non-radial-hazard and high contrast.However,its relatively slow imaging speed is a major factor affecting MRI clinical throughput and imaging quality.Changing the way of magnetic resonance data acquisition to increase the imaging speed by a data acquisition method much smaller than the Nyquist sampling law is an effective solution to this problem.The theoretical basis of this method is Compressed Sensing(CS).theory.Compressed sensing theory utilizes the sparsity of the signal,randomly acquiring the discrete samples,and then recovers the signal through a nonlinear reconstruction algorithm.In recent years,with the framework of CS theory,researchers have explored the sparsity of MR data from multiple angles.Combining with regularization constraints,they have proposed many methods for accelerating the magnetic resonance imaging,such as Total Variation(TV),Total Generalized Variation(TGV),Sparsity and Low Rank(SLR),etc.,this paper mainly studies the CS MR image reconstruction method based on the low-rank matrix constraint.The reconstruction of magnetic resonance images can be summarized as solving the ill-posed inverse problem of the original signal from the degraded signal,which is the core problem in this paper.This paper first establishes a reconstruction model of the degraded signal,and constrains the optimization model by constructing a lowrank matrix to convert it from the ill-posed problem to the well-posed problem which could be solved.For the optimization of the reconstructed model,commonly used methods include Singular Value Thresholding(SVT)and Iteratively Reweighted Least Squares(IRLS).However,since these two methods need to use singular value decomposition.When the large-scale matrix low rank constrained optimization problem is solved,it will lead to high computational complexity.In order to balance the effectiveness of the algorithm with the computational complexity,the Alternating Direction Method of Multipliers(ADMM)is mainly used to solve the optimization problem in this paper.Improving image reconstruction quality is the key to the study of magnetic resonance image reconstruction,this paper studies the 2D magnetic resonance image reconstruction method based on the low-rank constraint,discussing and analyzing the reconstruction quality and computational complexity.This paper studies the nonlocal low-rank constraint based on the non-local similarity in 2D MR images firstly,and uses the ADMM method to solve,effectively reconstructing the magnetic resonance image.In addition,this paper focuses on the reconstruction of 2D magnetic resonance images based on a structured low-rank matrix estimation model,and proposes an Adaptive Structured Low-Rank(ASLR)approach,which improves the image quality than the existing first-order method.The first-order structured lowrank reconstruction method is based on the hypothesis that MR image is the sum of the block constants,and the low-rank matrix constructed by the k-space data of the image is used as a regularization constraint.The ASLR method is used for more precise expression.The magnetic resonance image is assumed to be the sum of the block constant and the block linear function.The low rank of the matrix constructed by these two parts of data is used as the constraint term to balance the edge information and the smoothing information to achieve better reconstruction results.Finally,this paper studies the dynamic magnetic resonance reconstruction method based on low rank constraint.In addition to correlation of spatial information,the dynamic magnetic resonance image has correlation in the time domain.Thus,this paper studies the magnetic resonance image reconstruction algorithm based on low rank-sparse constraints and compared with the method using low rank information independently,it has a better reconstruction quality.In addition,the SLRA model is also transferred to the dynamic MRI.Compared with the method based on the firstorder structured low-rank method,the reconstructed method based on the adaptive structured low-rank method produces better reconstruction results and achieves high reconstruction quality at high sampling rate.