基于稀疏与低秩的动态核磁共振图像重建
发布时间：2019-05-11 15:41
【摘要】：动态核磁共振成像(Magnetic Resonance Imaging,MRI)能够提供对运动器官进行辅助诊断的图像,因此是一门非常有用的技术并且已经被广泛地应用于临床辅助诊断。然而,MRI过程通常需要花费很长的时间去扫描以获得成像数据,这个缺点限制了动态MRI图像可获得的时空分辨率。为此,压缩感知理论被引入到动态MRI当中去减少扫描时间,它的理论依据是:当一个信号是稀疏或转换稀疏时,它可以从部分不完整的测试数据中完美地重构出来。所以利用压缩感知(Compressed Sensing,CS)理论对欠采样的动态MRI数据重建可以加快成像速度。近些年,低秩矩阵补全理论将压缩感知理论从向量延伸到了矩阵,它能够将一个低秩矩阵的缺失或毁坏部分恢复。由于动态磁共振图像序列的帧与帧之间的相关性,低秩矩阵补全的思想可以被应用到欠采样的动态MRI的重建当中。本文的研究重点是如何利用压缩感知和低秩矩阵补全理论对欠采样的动态MRI数据进行重建,主要工作如下:首先,我们提出了一种将局部和全局低秩性相结合的动态MRI重建算法。由于动态MRI的空间和时间维都存在很大的相关性,若这些相关性能够在图像重建的过程中被有效地利用,则能够提高重建图像的时空分辨率。本文中,我们通过将3D动态MRI图像序列的每一帧向量化之后获得一个2D矩阵,然后再从这个2D矩阵中提取重叠的块。对于每一个提取的块,我们在一个局部的窗内寻找一定数量的相似块并由它们组成一个低秩矩阵,然后再使用一个非凸函数来估计这些低秩矩阵。至此,我们充分利用了时间维的局部相关性,为了获得更好的图像质量,我们使用了核范数对时间维的全局相关性进行了低秩惩罚。最后通过和一些最先进的方法进行对比,验证了我们提出的算法的高效性。然后,我们又提出了一种基于低秩约束和3D稀疏转换的将图像背景和前景分离的动态MRI重建算法。由于动态MRI和视频序列的相似性,所以它可以被看成是背景元素和动态元素的结合,因此我们基于鲁棒的主成分分析(Robust PrincipalComponent Analysis,RPCA)思想将它分解成了背景和动态元素两部分,再分别进行重建。对于背景部分,我们利用了一个基于块的非凸约束去对它进行低秩约束;而动态元素部分,我们则是采用了一个3D稀疏转换对它进行稀疏约束。然后我们使用了变量分离和交替优化算法对提出的优化问题进行了求解,可以分别得到背景部分和前景部分的解,只要将两者相加就可以获得最终的重建图像。实验结果表明,提出的这个算法可以恢复出更清晰的图像,并且图像的细节也保存得更好。
[Abstract]:Dynamic nuclear magnetic resonance imaging (Magnetic Resonance Imaging,MRI) can provide images of auxiliary diagnosis of motor organs, so it is a very useful technique and has been widely used in clinical auxiliary diagnosis. However, the MRI process usually takes a long time to scan to obtain imaging data, which limits the temporal and spatial resolution available to dynamic MRI images. Therefore, compression perception theory is introduced into dynamic MRI to reduce scanning time. Its theoretical basis is that when a signal is sparse or transformed sparse, it can be perfectly reconstructed from some incomplete test data. Therefore, compressed sensing (Compressed Sensing,CS) theory can be used to reconstruct undersampled dynamic MRI data to speed up the imaging speed. In recent years, the low rank matrix completion theory extends the compressed perception theory from vector to matrix, which can restore the missing or destroyed part of a low rank matrix. Because of the correlation between frames and frames in dynamic magnetic resonance image sequences, the idea of low rank matrix completion can be applied to the reconstruction of undersampled dynamic MRI. The focus of this paper is how to reconstruct the undersampled dynamic MRI data by using compressed perception and low rank matrix completion theory. The main work is as follows: first, We propose a dynamic MRI reconstruction algorithm which combines local and global low rank. Because there is a great correlation between the spatial and temporal dimensions of dynamic MRI, if these correlation can be effectively used in the process of image reconstruction, the spatial and temporal resolution of the reconstructed image can be improved. In this paper, we obtain a 2D matrix by vector each frame of 3D dynamic MRI image sequence, and then extract overlapping blocks from the 2D matrix. For each extracted block, we look for a certain number of similar blocks in a local window and form a low rank matrix from them, and then use a nonconvex function to estimate these low rank matrices. So far, we make full use of the local correlation of time dimension. In order to obtain better image quality, we use kernel norm to punish the global correlation of time dimension with low rank. Finally, the efficiency of the proposed algorithm is verified by comparing with some of the most advanced methods. Then, we propose a dynamic MRI reconstruction algorithm based on low rank constraint and 3D sparse transformation to separate the background and foreground of the image. Because of the similarity between dynamic MRI and video sequence, it can be regarded as the combination of background element and dynamic element, so we decompose it into two parts based on robust principal component analysis (Robust PrincipalComponent Analysis,RPCA). Then the reconstruction was carried out separately. For the background part, we use a block-based nonconvex constraint to constrain it with low rank, while in the dynamic element part, we use a 3D sparse transformation to sparse it. Then we use variable separation and alternating optimization algorithm to solve the proposed optimization problem, and we can get the solution of the background part and the foreground part respectively, and the final reconstruction image can be obtained by adding the two algorithms. The experimental results show that the proposed algorithm can restore clearer images and save the details of the images better.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41
本文编号：2474621
[Abstract]:Dynamic nuclear magnetic resonance imaging (Magnetic Resonance Imaging,MRI) can provide images of auxiliary diagnosis of motor organs, so it is a very useful technique and has been widely used in clinical auxiliary diagnosis. However, the MRI process usually takes a long time to scan to obtain imaging data, which limits the temporal and spatial resolution available to dynamic MRI images. Therefore, compression perception theory is introduced into dynamic MRI to reduce scanning time. Its theoretical basis is that when a signal is sparse or transformed sparse, it can be perfectly reconstructed from some incomplete test data. Therefore, compressed sensing (Compressed Sensing,CS) theory can be used to reconstruct undersampled dynamic MRI data to speed up the imaging speed. In recent years, the low rank matrix completion theory extends the compressed perception theory from vector to matrix, which can restore the missing or destroyed part of a low rank matrix. Because of the correlation between frames and frames in dynamic magnetic resonance image sequences, the idea of low rank matrix completion can be applied to the reconstruction of undersampled dynamic MRI. The focus of this paper is how to reconstruct the undersampled dynamic MRI data by using compressed perception and low rank matrix completion theory. The main work is as follows: first, We propose a dynamic MRI reconstruction algorithm which combines local and global low rank. Because there is a great correlation between the spatial and temporal dimensions of dynamic MRI, if these correlation can be effectively used in the process of image reconstruction, the spatial and temporal resolution of the reconstructed image can be improved. In this paper, we obtain a 2D matrix by vector each frame of 3D dynamic MRI image sequence, and then extract overlapping blocks from the 2D matrix. For each extracted block, we look for a certain number of similar blocks in a local window and form a low rank matrix from them, and then use a nonconvex function to estimate these low rank matrices. So far, we make full use of the local correlation of time dimension. In order to obtain better image quality, we use kernel norm to punish the global correlation of time dimension with low rank. Finally, the efficiency of the proposed algorithm is verified by comparing with some of the most advanced methods. Then, we propose a dynamic MRI reconstruction algorithm based on low rank constraint and 3D sparse transformation to separate the background and foreground of the image. Because of the similarity between dynamic MRI and video sequence, it can be regarded as the combination of background element and dynamic element, so we decompose it into two parts based on robust principal component analysis (Robust PrincipalComponent Analysis,RPCA). Then the reconstruction was carried out separately. For the background part, we use a block-based nonconvex constraint to constrain it with low rank, while in the dynamic element part, we use a 3D sparse transformation to sparse it. Then we use variable separation and alternating optimization algorithm to solve the proposed optimization problem, and we can get the solution of the background part and the foreground part respectively, and the final reconstruction image can be obtained by adding the two algorithms. The experimental results show that the proposed algorithm can restore clearer images and save the details of the images better.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41
【参考文献】
相关期刊论文 前2条
1 王聪;冯衍秋;;利用GPGPU进行快速稀疏磁共振数据重建[J];计算机工程与应用;2011年17期
2 杨海蓉;张成;丁大为;韦穗;;压缩传感理论与重构算法[J];电子学报;2011年01期
，本文编号：2474621
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