基于压缩感知的MRI图像的快速重建

发布时间：2018-07-31 07:11

【摘要】：磁共振成像(MRI)技术是一种可以对活体器官和组织做出详细的器官和组织图像的医疗成像手段,其优势是对人体无损伤、无辐射等伤害。但是MRI的不足是成像速度慢,目前有两种方法可以解决这个不足,方法一是采用对硬件进行改进,例如利用多线圈进行成像、设计快速阶梯矩阵序列等;方法二通过减少K空间数据的采集量,再利用重建算法进行图像重建,此方法又称K空间重建。其中部分K空间重建不需要对硬件进行改进,只需要对K空间重建算法改进即可达到提高成像速度的目的。由于稀疏表示和压缩感知理论的发展为通过对K空间的数据有效的重建MRI图像提供了强有力的理论基础,由部分K空间数据重建MRI图像本质上是一种对反问题求解,即通过少量的K空间数据求出完整的K空间数据的过程,而反问题求解的关键是利用有效先验信息。本文主要研究图像中的先验信息,再结合快速的重建算法进行重建,并且设计了有效的循环测量矩阵,主要内容如下:(1)压缩感知磁共振成像测量矩阵的设计需要满足与稀疏变换矩阵的非相干性,同时还要保证能够应用到硬件。本文从循环测量矩阵生成元素的相位和幅值两个方面研究优化并构造了循环测量矩阵,提出了交替循环寻优方式生成元素的幅值再结合混沌的随机相位,以此来实现循环测量矩阵的优化。再和现有的循环矩阵进行比较,本文构造的循环测量矩阵对应的等价字典列向量之间的互相干性更低,在测量数据相同的情况下,重建图像的质量更好。(2)曲波分析是一种方向性多尺度的分析方法,它是在小波分析和脊波分析的基础上发展而来的。构建的曲波变换能够强化图像的边缘以及解决图像跳跃性奇异点的问题。交替方向乘子算法(Alternating Direction Method of Multipliers,简称ADMM)可有效的解决可分离凸规划问题,通过对目标函数的1l范数进行迭代,从而降低算法的计算复杂度,加快了算法的收敛时间。本文在交替乘子算法的基础上,利用曲波变换、全变差作为正则项,对压缩感知磁共振图像进行重建。此方法能够充分挖掘磁共振图像在不同变换域中的不同特征的稀疏性,在测量矩阵相同的基础上,重建质量得到了提升。
[Abstract]:Magnetic resonance imaging (MRI) is a kind of medical imaging method which can make detailed organ and tissue images of living organs and tissues. Its advantage is that it has no harm to human body and radiation. However, the disadvantage of MRI is that the imaging speed is slow. There are two methods to solve this problem. The first method is to improve the hardware, such as using multi-coil imaging, designing the fast step matrix sequence and so on. Second, by reducing the amount of K spatial data acquisition, and then using the reconstruction algorithm for image reconstruction, this method is also called K space reconstruction. Some of the K-space reconstruction do not need to improve the hardware, only need to improve the K-space reconstruction algorithm to achieve the purpose of improving the imaging speed. As the development of sparse representation and compressed perception theory provides a strong theoretical basis for the efficient reconstruction of MRI images from K-space data, the reconstruction of MRI images from partial K-space data is essentially a kind of inverse problem solving. That is to say, the process of finding complete K spatial data through a small amount of K spatial data, and the key to solve inverse problem is to use effective prior information. This paper mainly studies the priori information in the image, and then combines the fast reconstruction algorithm to reconstruct the image, and designs an effective cycle measurement matrix. The main contents are as follows: (1) the design of the compressed perceptual magnetic resonance imaging measurement matrix needs to satisfy the non-coherence with the sparse transformation matrix and ensure that it can be applied to the hardware at the same time. In this paper, the phase and amplitude of the elements generated by the cyclic measurement matrix are studied and optimized, and the cyclic measurement matrix is constructed. The alternating cycle optimization method is proposed to generate the amplitudes of the elements combined with the random phase of chaos. In this way, the circulatory measurement matrix is optimized. Compared with the existing cyclic matrix, the corresponding equivalent dictionary column vector of the circular measurement matrix constructed in this paper has lower coherence, and the same measurement data is obtained. The quality of reconstructed image is better. (2) Qu Bo analysis is a directional multi-scale analysis method which is developed on the basis of wavelet analysis and ridgelet analysis. The constructed Qu Bo transform can enhance the edge of the image and solve the problem of jumping singularity. The alternating direction multiplier algorithm (Alternating Direction Method of Multipliers,) can effectively solve the separable convex programming problem. By iterating the 1l norm of the objective function, the computational complexity of the algorithm is reduced and the convergence time of the algorithm is accelerated. In this paper, based on the alternating multiplier algorithm, the compressed perceptual magnetic resonance image is reconstructed by using Qu Bo transform and total variation as the regular term. This method can fully exploit the sparsity of different features of magnetic resonance images in different transform domains, and the reconstruction quality is improved on the basis of the same measurement matrix.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：R445.2;TP391.41

【参考文献】