基于扩散张量成像的扩散张量估算及相关技术研究
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摘要
扩散张量成像是20世纪90年代发展起来的一种新的核磁共振成像技术,是目前世界上唯一能够无创检测活体组织中水分子扩散情况的医学成像技术。它能够提供人体的组织结构信息以及大脑白质纤维束的分布信息,对于大脑皮质及皮质下白质纤维的研究以及大脑的多种疾病如肿瘤、梗死、认知等研究都有其独特的优势。因而在医学成像领域中具有非常大的应用前景。
本文对扩散张量成像的张量估算及相关技术研究主要包括三个方面：扩散张量图像中的噪声的特点及其对扩散张量成像的影响研究、扩散张量图像的张量估算方法的研究、扩散张量图像的降噪方法的研究。首先根据核磁共振扩散张量成像的机理,对扩散张量图像中噪声的分布特性及其对扩散张量图像的影响进行了分析。研究中通过对扩散张量图像中的噪声来源进行深入分析,并在此基础上建立了扩散张量图像的莱斯噪声模型,同时基于该含噪模型提出了采用矩估计的方法对核磁共振扩散张量图像的噪声进行估算,这种方法能够更加有效地对扩散张量的噪声进行估计。进一步,我们在该含噪模型的基础上通过蒙特卡罗仿真实验深入分析扩散张量图像及其导出量如张量各向异性值(Fractional Anisotropy FA)及张量迹(Trace)等参数值在噪声影响下产生的偏差,总结了扩散张量特性在不同噪声下的变化规律,这些规律对于图像的校正、分析及诊断都具有非常重要的意义。其次,在扩散张量的估计方面,我们针对扩散张量图像的成像原理,建立扩散张量的估算模型。并针对图像中的异常数据的特点及其对张量估算的影响进行分析。同时对张量估算领域中经典的最小二乘估计法进行了深入研究,针对最小二乘估计法稳健性比较差的特点提出了将M估计、HBP估计及MM估计等稳健估计算法应用于扩散张量的估算中,并对各估计算法在扩散张量估计中的效果进行分析比较,采用模拟以及真实数据进行实验验证,通过实验发现：在扩散张量的估算中,稳健估计算法中的MM估计兼具非常好的稳健性及估计效率,较其他算法能够得到更好的张量估计结果。最后,我们基于扩散张量图像的特点,对非线性及线性滤波器在扩散张量图像降噪中的应用进行研究。由于扩散张量图像的噪声为莱斯噪声、数据量非常大并且对数据要求进行实时处理,所以要求用于扩散张量图像降噪的滤波器能够较好的保留图像边界并且运算简单。根据这些特点,我们对维纳滤波器在扩散张量图像降噪中的应用进行了深入分析,针对维纳滤波器在保留图像边界和不能有效去除莱斯噪声等方面的不足提出了邻域偏移算法以及莱斯校正算法。并进一步采用邻域偏移算法及莱斯校正算法对维纳滤波器进行修正,从而使其更好地适用于对扩散张量图像的降噪处理。我们通过模拟数据及真实数据的实验对各降噪算法的降噪效果进行比较,通过实验结果我们发现修正维纳滤波器在具有较好地实时降噪的前提下,能够更加有效地对扩散张量图像进行降噪。
Diffusion Tensor Imaging, the sole medical imaging technology capable of non-invasively examining the diffusion of water molecules in vivo, is a new nuclear magnetic resonance imaging technique arising in1990s. DTI has its unique advantages in the study of cerebral cortex, white matter tractography and that of various brain diseases as tumor, infarct, cognition, and etc., and thus has quite an extensive application prospect in medical imaging fields.
This dissertation presents a thorough study, of the estimation of diffusion tensor, the denoising of DTI (Diffusion Tensor Images), the characters of its noisy field, the effect of noise on diffusion tensor. Firstly, the distributing characteristics of noise fields in DTI and the effect of the noise on diffusion tensor have been analyzed. The model of Rician noise has been built based on the analysis of the noise in DTI. And then the method of moment estimation has been proposed to be applied in the estimation of noise field, which is more effective. Meanwhile, based on this noise model, a Monte Carlo simulation experiment has been performed to make a thorough analysis of the bias caused by the noise in DTI and its indices (such as Fractional Anisotropy and Trace). The experiment leads to summarizing the variation laws of the features of diffusion tensor varying according to the noise variation, which are significant in analyzing and diagnosing medical images.
Secondly, based on the character of diffusion technology, a model of tensor estimation, the features of the outlier caused by noise and its effect on diffusion tensor estimation have been analyzed. Meanwhile, after a thorough study of the classic least squared method in the fields of diffusion tensor estimation shows, some more robust estimators such as M estimator, HBP estimator and MM estimator are proposed to be applied in the estimating process of the diffusion tensor due to the founding due to the bad robustness of least squared methods. Moreover, the respective features of these different robust estimators have been analyzed and the consequent estimating results have been compared through Monte Carlo simulation experiment and real data experiment. The result shows that the MM estimator performs better in contrast to other estimators because it is more robust and more efficient.
Lastly, a research on denoising DTI has been carried out. During this research, the linear and non-linear DTI denoising methods have been analyzed and applied. As the noise of DTI is Rician distribution and the amount of DTI data is quite enormous and requires being real-time processed, the denosing method applied in DTI should be concise and capable of preserving boundary signals effectively. According these requirements, the wiener method has been proposed to be applied to the denoising of DTI and then further analyzed. Moreover, a local shift method has been proposed to make wiener filter dispose boundary signals better and the method of Rician correction has been applied to the DTI. The application of local shift method and Ricain correction method makes the wiener filter denoise DTI more effectively. The result obtained from comparing the respective effects of different denoising methods through simulated and real data experiments shows that the modified wiener filter is faster and more effectively.
本文对扩散张量成像的张量估算及相关技术研究主要包括三个方面：扩散张量图像中的噪声的特点及其对扩散张量成像的影响研究、扩散张量图像的张量估算方法的研究、扩散张量图像的降噪方法的研究。首先根据核磁共振扩散张量成像的机理,对扩散张量图像中噪声的分布特性及其对扩散张量图像的影响进行了分析。研究中通过对扩散张量图像中的噪声来源进行深入分析,并在此基础上建立了扩散张量图像的莱斯噪声模型,同时基于该含噪模型提出了采用矩估计的方法对核磁共振扩散张量图像的噪声进行估算,这种方法能够更加有效地对扩散张量的噪声进行估计。进一步,我们在该含噪模型的基础上通过蒙特卡罗仿真实验深入分析扩散张量图像及其导出量如张量各向异性值(Fractional Anisotropy FA)及张量迹(Trace)等参数值在噪声影响下产生的偏差,总结了扩散张量特性在不同噪声下的变化规律,这些规律对于图像的校正、分析及诊断都具有非常重要的意义。其次,在扩散张量的估计方面,我们针对扩散张量图像的成像原理,建立扩散张量的估算模型。并针对图像中的异常数据的特点及其对张量估算的影响进行分析。同时对张量估算领域中经典的最小二乘估计法进行了深入研究,针对最小二乘估计法稳健性比较差的特点提出了将M估计、HBP估计及MM估计等稳健估计算法应用于扩散张量的估算中,并对各估计算法在扩散张量估计中的效果进行分析比较,采用模拟以及真实数据进行实验验证,通过实验发现：在扩散张量的估算中,稳健估计算法中的MM估计兼具非常好的稳健性及估计效率,较其他算法能够得到更好的张量估计结果。最后,我们基于扩散张量图像的特点,对非线性及线性滤波器在扩散张量图像降噪中的应用进行研究。由于扩散张量图像的噪声为莱斯噪声、数据量非常大并且对数据要求进行实时处理,所以要求用于扩散张量图像降噪的滤波器能够较好的保留图像边界并且运算简单。根据这些特点,我们对维纳滤波器在扩散张量图像降噪中的应用进行了深入分析,针对维纳滤波器在保留图像边界和不能有效去除莱斯噪声等方面的不足提出了邻域偏移算法以及莱斯校正算法。并进一步采用邻域偏移算法及莱斯校正算法对维纳滤波器进行修正,从而使其更好地适用于对扩散张量图像的降噪处理。我们通过模拟数据及真实数据的实验对各降噪算法的降噪效果进行比较,通过实验结果我们发现修正维纳滤波器在具有较好地实时降噪的前提下,能够更加有效地对扩散张量图像进行降噪。
Diffusion Tensor Imaging, the sole medical imaging technology capable of non-invasively examining the diffusion of water molecules in vivo, is a new nuclear magnetic resonance imaging technique arising in1990s. DTI has its unique advantages in the study of cerebral cortex, white matter tractography and that of various brain diseases as tumor, infarct, cognition, and etc., and thus has quite an extensive application prospect in medical imaging fields.
This dissertation presents a thorough study, of the estimation of diffusion tensor, the denoising of DTI (Diffusion Tensor Images), the characters of its noisy field, the effect of noise on diffusion tensor. Firstly, the distributing characteristics of noise fields in DTI and the effect of the noise on diffusion tensor have been analyzed. The model of Rician noise has been built based on the analysis of the noise in DTI. And then the method of moment estimation has been proposed to be applied in the estimation of noise field, which is more effective. Meanwhile, based on this noise model, a Monte Carlo simulation experiment has been performed to make a thorough analysis of the bias caused by the noise in DTI and its indices (such as Fractional Anisotropy and Trace). The experiment leads to summarizing the variation laws of the features of diffusion tensor varying according to the noise variation, which are significant in analyzing and diagnosing medical images.
Secondly, based on the character of diffusion technology, a model of tensor estimation, the features of the outlier caused by noise and its effect on diffusion tensor estimation have been analyzed. Meanwhile, after a thorough study of the classic least squared method in the fields of diffusion tensor estimation shows, some more robust estimators such as M estimator, HBP estimator and MM estimator are proposed to be applied in the estimating process of the diffusion tensor due to the founding due to the bad robustness of least squared methods. Moreover, the respective features of these different robust estimators have been analyzed and the consequent estimating results have been compared through Monte Carlo simulation experiment and real data experiment. The result shows that the MM estimator performs better in contrast to other estimators because it is more robust and more efficient.
Lastly, a research on denoising DTI has been carried out. During this research, the linear and non-linear DTI denoising methods have been analyzed and applied. As the noise of DTI is Rician distribution and the amount of DTI data is quite enormous and requires being real-time processed, the denosing method applied in DTI should be concise and capable of preserving boundary signals effectively. According these requirements, the wiener method has been proposed to be applied to the denoising of DTI and then further analyzed. Moreover, a local shift method has been proposed to make wiener filter dispose boundary signals better and the method of Rician correction has been applied to the DTI. The application of local shift method and Ricain correction method makes the wiener filter denoise DTI more effectively. The result obtained from comparing the respective effects of different denoising methods through simulated and real data experiments shows that the modified wiener filter is faster and more effectively.
引文
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