基于稀疏表达的人体心脏磁共振扩散张量图像的去噪研究
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摘要
磁共振扩散张量成像（Magnetic Resonance Diffusion Tensor Imaging, DT-MRI）能够在分子水平上提供生物组织的功能性信息，是当前研究活体组织纤维结构的唯一非入侵方法。基于DT-MRI的人体心脏功能性分析和心肌纤维束重建是一个全新的课题，将其用于研究心血管疾病的扩散张量特性改变和纤维结构的病理学变异，具有重要的临床意义和社会经济效益。但是，心脏DT-MRI技术极易受噪声的干扰，并且采集到的扩散加权信号强度较弱，使得扩散加权图像的信噪比和对比度都低于普通磁共振图像。如果不能有效的滤除图像中的噪声，则计算得到的扩散张量的准确性就无法保证，这将极大的降低心肌纤维结构信息获取与重构的可行性，制约了心脏DT-MRI技术的发展。本课题将研究基于稀疏表达的人体心脏DT-MRI的去噪，这是心脏DT-MRI应用首先要解决的关键问题。
基本稀疏表达去噪算法应用于心脏DT-MRI图像去噪时，对正则化程度低的区域容易滤波不足，并且产生去噪伪影。针对这个问题，提出一种参数自适应的变分正则化约束稀疏去噪算法。自适应参数能够依据各点的滤波程度调节保真项和平滑项的权重，从而将去噪过程中残留的噪声和伪影通过正则项滤除，将丢失的结构信息通过保真项进行补偿，提高了稀疏表达的去噪效果。
为了提高具有多成分特性的心脏DT-MRI图像与字典的匹配度，改善非稳定点对应的图像结构特征的去噪效果，提出一种多成分图像的分区稀疏去噪算法。根据图像的非稳定度，将多成分图像分割为不同的单元，并且为不同成分间的过渡区域构造结构自适应的阶跃原子。采用DCT函数、Haar函数和结构自适应阶跃原子组成混合字典，对各单元分别进行去噪处理。
利用心脏DT-MRI序列中相邻层图像的空间相关性，提出一种序列图像的三维稀疏去噪算法。该算法把稀疏去噪扩展到三维空间，并且采用K-SVD数据训练算法构造特征自适应的三维字典，使得三维原子具有与三维图像相一致的空间相关性。算法适用于心脏DT-MRI序列的稀疏去噪，能够有效的保留各层独有的特征，恢复图像的细节信息。
基于心脏DT-MRI图像的自相似性与稀疏性间的隐含关系，提出基于图像自相似性的结构自适应稀疏去噪算法。该算法定义了一种具有阈值约束的相似性测度，在此基础上，将图像中的相似块聚合成三维数据，采用结构自适应窗从相似块集合中提取出结构自适应三维数据，应用主成分分析对三维数据做变换域去噪。算法适用于结构冗余度高的图像，避免了去噪伪影，实现了去噪图像对比度和平滑性的平衡。
最后，采用离体的人体心脏DT-MRI，对本文提出的稀疏去噪算法进行实验验证。为了评定心肌扩散张量数据的去噪效果，提出一种融合局部拟合能量和梯度敏感能量的水平集分割算法，应用于心肌的三维重建。实验结果表明，对心脏DT-MRI图像去噪后，可以减少非正定张量的个数，提高心肌扩散张量的准确性和主特征向量场的正则化程度，降低部分各向异性指标的均值，增大方向相关系数的均值，提高纤维束重构的可信度。
Since magnetic resonance diffusion tensor imaging (DT-MRI) can provide thefunctional information of biological organization at the molecular level, it is theonly non-invasive way of fiber structure detection for in vivo tissue in the currentresearch. Today DT-MRI has been applied to the research on brain, spinal cord,liver and muscle for diagnosis of their micro-structures, which have achieved goodpreliminary results. However, the analysis of human heart functions and heart fiberreconstruction based on DT-MRI are still new research areas to be developed.There are important clinical significance and potential social economic benefits toapply DT-MRI to study the diffusion tensor characteristics and fiber structure of thepathological changes for various cardiovascular diseases.
Because of noise interference, the intensity of diffusion weighted data is weakfor DT-MRI techniques. Hence the signal-to-noise ratio and contrast are lower thannormal MRI. If reliable information can not be obtained from the data, the accuracylevel of the calculated diffusion tensor is questionable, thus greatly affecting theinformation acquisition of myocardium fiber structure and reducing fiberreconstruction feasibility. Accordingly, this thesis aims towards the study of a heartDT-MRI denoising technique based on sparse representation, which is one of theprimary and difficult issues to be resolved for the development of heart DT-MRItechniques.
For classical sparse denoising algorithm, some of the noise are represented asimage features and thus inducing artifacts. This negative effect is particularlysignificant in image regions with low regularization degree. Therefore, a totalvariation regularization is introduced into the sparse denoising model, and aparameter adaptive total variation based sparse representation denoising algorithmis proposed. The adaptive parameter can adjust the weight between denoising termand fidelity term according to the filtering level of each point, which allows forsuppressing the residual noise and artifacts and compensating the lost structureinformation. Thus, the denoising results can be improved compared with classicalsparse denoising algorithm.
According to the multi-component characteristic of human heart DT-MRI, amulti-component image partition sparse denoising algorithm is developed. Theimage will be divided into different partitions based on the non-stationary degree,and a set of structure adaptive step atoms are designed for transition region between different partitions. Then a mixed dictionary composed of DCT basis, Haar basisand structure adaptive step atoms is constructed. Finally, the denoising isimplemented on each partition separately. This algorithm has good performance indenoising image features and non-stationary points by improving the matchingdegree between images and dictionaries.
Considering the spatial correlation in cardiac DT-MRI sequence images, thisresearch proposes a3D sparse denoising algorithm for sequence images as well as aK-SVD based data training algorithm for the design of a3D structure adaptivedictionary, which enables the3D atoms have coherent spatial correlations with3Dimages. In this way, the sparse representation denoising is extended into3D spacetaking advantage of the structure similarity between neighbor slices. This algorithmshould be applied for DT-MRI sequence images denoising and it can preserve theunique fine structures of each slice effectively.
Since cardiac DT-MRI images exhibit self-similarity, the study advances todevelop a structure adaptive sparse denoising algorithm on the basis of image self-similarity. A new similarity measurement with a threshold constraint is defined. Onthis basis, similar patches are searched from the image and grouped into3D data.However, this thesis implements structure adaptive3D data extracted from squarepatches with a structure adaptive window. Finally, principal component analysis isused to denoising the3D data in transform domain. This algorithm has goodperformance in denoising images with high structural redundancy. It can achieve atrade-off between image contrast and smoothness while preventing artifacts indenoising.
Denoising human heart DT-MRI with sparse representation is examined andanalyzed in this research. As the basis for myocardium diffusion tensor analysis andDT-MRI denoising assessment, a level set segmentation method combining localfitting energy and gradient sensitivity energy is proposed. Myocardiums can besegmented successfully from ex vivo heart DT-MRI using this method whichenables the myocardium3D reconstruction. Experimental results show that thedenoising of heart DT-MRI can reduce the number of non-positive definite tensors,improve the accuracy of myocardial diffusion tensors and the regularization ofprincipal eigenvector fields, lower fractional anisotropy mean, increase coherenceindex mean, and finally improve the reliability of myocardium fiber reconstruction.
基本稀疏表达去噪算法应用于心脏DT-MRI图像去噪时，对正则化程度低的区域容易滤波不足，并且产生去噪伪影。针对这个问题，提出一种参数自适应的变分正则化约束稀疏去噪算法。自适应参数能够依据各点的滤波程度调节保真项和平滑项的权重，从而将去噪过程中残留的噪声和伪影通过正则项滤除，将丢失的结构信息通过保真项进行补偿，提高了稀疏表达的去噪效果。
为了提高具有多成分特性的心脏DT-MRI图像与字典的匹配度，改善非稳定点对应的图像结构特征的去噪效果，提出一种多成分图像的分区稀疏去噪算法。根据图像的非稳定度，将多成分图像分割为不同的单元，并且为不同成分间的过渡区域构造结构自适应的阶跃原子。采用DCT函数、Haar函数和结构自适应阶跃原子组成混合字典，对各单元分别进行去噪处理。
利用心脏DT-MRI序列中相邻层图像的空间相关性，提出一种序列图像的三维稀疏去噪算法。该算法把稀疏去噪扩展到三维空间，并且采用K-SVD数据训练算法构造特征自适应的三维字典，使得三维原子具有与三维图像相一致的空间相关性。算法适用于心脏DT-MRI序列的稀疏去噪，能够有效的保留各层独有的特征，恢复图像的细节信息。
基于心脏DT-MRI图像的自相似性与稀疏性间的隐含关系，提出基于图像自相似性的结构自适应稀疏去噪算法。该算法定义了一种具有阈值约束的相似性测度，在此基础上，将图像中的相似块聚合成三维数据，采用结构自适应窗从相似块集合中提取出结构自适应三维数据，应用主成分分析对三维数据做变换域去噪。算法适用于结构冗余度高的图像，避免了去噪伪影，实现了去噪图像对比度和平滑性的平衡。
最后，采用离体的人体心脏DT-MRI，对本文提出的稀疏去噪算法进行实验验证。为了评定心肌扩散张量数据的去噪效果，提出一种融合局部拟合能量和梯度敏感能量的水平集分割算法，应用于心肌的三维重建。实验结果表明，对心脏DT-MRI图像去噪后，可以减少非正定张量的个数，提高心肌扩散张量的准确性和主特征向量场的正则化程度，降低部分各向异性指标的均值，增大方向相关系数的均值，提高纤维束重构的可信度。
Since magnetic resonance diffusion tensor imaging (DT-MRI) can provide thefunctional information of biological organization at the molecular level, it is theonly non-invasive way of fiber structure detection for in vivo tissue in the currentresearch. Today DT-MRI has been applied to the research on brain, spinal cord,liver and muscle for diagnosis of their micro-structures, which have achieved goodpreliminary results. However, the analysis of human heart functions and heart fiberreconstruction based on DT-MRI are still new research areas to be developed.There are important clinical significance and potential social economic benefits toapply DT-MRI to study the diffusion tensor characteristics and fiber structure of thepathological changes for various cardiovascular diseases.
Because of noise interference, the intensity of diffusion weighted data is weakfor DT-MRI techniques. Hence the signal-to-noise ratio and contrast are lower thannormal MRI. If reliable information can not be obtained from the data, the accuracylevel of the calculated diffusion tensor is questionable, thus greatly affecting theinformation acquisition of myocardium fiber structure and reducing fiberreconstruction feasibility. Accordingly, this thesis aims towards the study of a heartDT-MRI denoising technique based on sparse representation, which is one of theprimary and difficult issues to be resolved for the development of heart DT-MRItechniques.
For classical sparse denoising algorithm, some of the noise are represented asimage features and thus inducing artifacts. This negative effect is particularlysignificant in image regions with low regularization degree. Therefore, a totalvariation regularization is introduced into the sparse denoising model, and aparameter adaptive total variation based sparse representation denoising algorithmis proposed. The adaptive parameter can adjust the weight between denoising termand fidelity term according to the filtering level of each point, which allows forsuppressing the residual noise and artifacts and compensating the lost structureinformation. Thus, the denoising results can be improved compared with classicalsparse denoising algorithm.
According to the multi-component characteristic of human heart DT-MRI, amulti-component image partition sparse denoising algorithm is developed. Theimage will be divided into different partitions based on the non-stationary degree,and a set of structure adaptive step atoms are designed for transition region between different partitions. Then a mixed dictionary composed of DCT basis, Haar basisand structure adaptive step atoms is constructed. Finally, the denoising isimplemented on each partition separately. This algorithm has good performance indenoising image features and non-stationary points by improving the matchingdegree between images and dictionaries.
Considering the spatial correlation in cardiac DT-MRI sequence images, thisresearch proposes a3D sparse denoising algorithm for sequence images as well as aK-SVD based data training algorithm for the design of a3D structure adaptivedictionary, which enables the3D atoms have coherent spatial correlations with3Dimages. In this way, the sparse representation denoising is extended into3D spacetaking advantage of the structure similarity between neighbor slices. This algorithmshould be applied for DT-MRI sequence images denoising and it can preserve theunique fine structures of each slice effectively.
Since cardiac DT-MRI images exhibit self-similarity, the study advances todevelop a structure adaptive sparse denoising algorithm on the basis of image self-similarity. A new similarity measurement with a threshold constraint is defined. Onthis basis, similar patches are searched from the image and grouped into3D data.However, this thesis implements structure adaptive3D data extracted from squarepatches with a structure adaptive window. Finally, principal component analysis isused to denoising the3D data in transform domain. This algorithm has goodperformance in denoising images with high structural redundancy. It can achieve atrade-off between image contrast and smoothness while preventing artifacts indenoising.
Denoising human heart DT-MRI with sparse representation is examined andanalyzed in this research. As the basis for myocardium diffusion tensor analysis andDT-MRI denoising assessment, a level set segmentation method combining localfitting energy and gradient sensitivity energy is proposed. Myocardiums can besegmented successfully from ex vivo heart DT-MRI using this method whichenables the myocardium3D reconstruction. Experimental results show that thedenoising of heart DT-MRI can reduce the number of non-positive definite tensors,improve the accuracy of myocardial diffusion tensors and the regularization ofprincipal eigenvector fields, lower fractional anisotropy mean, increase coherenceindex mean, and finally improve the reliability of myocardium fiber reconstruction.
引文
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