基于凸分析与优化的功能核磁共振成像数分析方法研究

发布时间：2018-05-08 01:19

本文选题：功能核磁共振成像 + 脑激活区定位　；参考：《华南理工大学》2014年博士论文

【摘要】：功能核磁共振成像(Functional Magnetic Resonance Imaging,fMRI)是一种重要的脑功能成像技术。它结合了功能、影像和解剖三方面的因素,是一种在活体人脑中定位脑功能区的有效方法。它具有诸多优势,如无创伤性、无放射性、较高的空间分辨率、可多次重复操作等。因此,fMRI技术已成为脑科学和生命科学研究中的重要工具。然而由于fMRI数据维数高,信噪比低,而且信号中混合了大量未知的脑活动模式,传统处理方法往往难以达到理想效果。多项研究表明,在fMRI数据的分析方法中,合理地利用fMRI数据的特点来引入一些可靠的先验信息,将有助于提高方法的性能。本论文主要目标是根据fMRI数据的一般特性,如数据的非负性、高维结构特性和脑激活区的空间稀疏特性等,利用非负信号盲分离、张量表示、以及信号稀疏表示等信号处理领域的前沿方法,建立基于凸分析与凸优化技术的算法框架,并将合理的先验信息以凸约束形式引入优化过程,从而提出高效的、适合高维大数据量的fMRI数据分析与处理的计算方法,实现对脑激活区的精确定位,并进行高教的神经解码。本论文的主要工作有以下几个方面：首先,以稀疏表示和张量分析为基础,结合fMRI数据的高维性特点,以张量形式建立了fMRI数据和任务函数之间的回归模型,并在此基础上提出了两种fMRI数据分析方法：一种是基于多维导数约束的鲁棒稀疏体素选择方法(Robust Voxel Selection Method with Multi-dimensional Derivative Constraints, RVSMDC);另一种是基于多维导数约束的鲁棒神经解码方法(Robust Sparse Decoding with Multi-dimensional Constraints, RSDMDC)。由于fMRI数据本身就是高阶张量,利用张量技术来构建fMRI数据分析方法能够很好地保持fMRI数据空间结构信息不被破坏,有助于提高算法对数据的分析能力。RVSMDC方法是针对体素选择分析而提出的。目前传统的稀疏表示方法在进行体素选择分析时,存在选择出的激活体素空间分布过于稀疏,较难形成团块(Cluster)的问题。对此,RVSMDC方法在稀疏表示优化问题中加入了多维偏导约束条件,以使得选择出的激活体素不但保持空间稀疏特性,还同时具有空间团块特点。此外,我们还在RVSMDC方法中引入了误差容忍机制来获取算法对fMRI模型误差的容忍能力。RSDMDC方法是针对解码分析而提出的。在解码分析中,解码准确率是一个重要的性能指标。为了获取较高的解码准确率,RSDMDC方法直接在优化目标函数中最小化fMRI数据与任务函数之间的回归误差,来获取最适合解码分析的回归系数。实验结果表明,RSDMDC方法能够取得较高的解码准确率。其次,以凸分析为基础,引入了基于非负性和稀疏性的盲分离方法,即非负源混合观测数据的凸分析方法(Convex Analysis of Mixtures of Non-negative Sources, CAMNS),并从分解得到分量中挑选出持续任务相关(Consist Task Related, CTR)分量来进一步进行体素选择和解码分析。由于大脑中复杂的多任务并行处理机制,fMRI数据中除了我们感兴趣的脑功能活动信号之外,还包含了大量未知脑活动信号。传统的盲分离(Blind Source Separation, BSS)方法,即独立成分分析(Independent Component Analysis, ICA)依靠其强大的数据挖掘能力,在探索未知脑活动模式的研究中取得了重要进展。然而近期研究表明,ICA方法的独立性数学假设在实际情况下很难完全满足,导致ICA算法对于fMRI数据分析性能的下降。在本文中,CAMNS方法主要利用fMRI信号本身具有的特性,如信号的非负性,来进行盲分解。借助于非负性和稀疏性数学假设,CAMNS方法构建了一个凸分析的框架来对源分量进行估计。这个过程是通过两个步骤来实现的。首先,该方法表明源分量在几何上可以看作是一个凸集合的端点,该凸集合可以由观测数据得到。其次,估计源分量的过程可以看作是确定上一步骤中所构建的凸集合端点的过程。此外,我们用分离得到的CTR分量进行进一步的体素选择和神经解码分析。实验结果表明,所提出的算法能够从数据中挖掘出更多有用信息,这是由于它采用了更符合fMRI数据特点的数学假设。最后,为了充分利用fMRI数据特点来发掘隐藏在fMRI数据中的有用信息,我们进一步探索如何将更多有用的数据特点转化为可靠的先验信息,并以凸约束方式引入分解算法中。为此,我们提出了基于字典稀疏性的盲分量方法。新方法利用fMRI数据的特点,将字典学习和稀疏表示结合起来。利用源分量在字典中的稀疏性,来将盲分离的过程转移到稀疏域中进行,这样的措施能够提高盲分离的质量。在新方法中,首先需要根据先验知识选择合适的字典,并利用预先选择的字典来将盲分离过程变换到稀疏域中,然后再利用源分量在稀疏域中的稀疏性约束来进行盲分解。选择一个合适的字典对于所提出方法的性能起着关键的作用。为了准确地从fMRI数据中提取出感兴趣的CTR分量,我们需要选择合适的字典来对CTR分量进行稀疏表示。在本文中,我们选择了小波变换字典。通过将脑激活信号用一小部分小波系数来表示,我们发现小波变换可以较好地对CTR分量中的脑激活信号进行稀疏表示。实验结果也表明,在CTR分量相关的稀疏域中进行盲分解能够提高提取CTR分量的准确性。此外,基于CTR分量的体素选择和解码分析也能够得到较好的结果。
[Abstract]:Functional Magnetic Resonance Imaging (fMRI) is an important brain functional imaging technique. It combines three aspects of function, image and anatomy. It is an effective method to locate the brain function in the living human brain. It has many advantages, such as non traumatic, non radioactive, and high spatial resolution. Therefore, fMRI technology has become an important tool in the research of brain science and life science. However, because of the high dimension of the fMRI data, the low signal to noise ratio, and a large number of unknown brain activity patterns mixed in the signal, the traditional processing methods are often difficult to achieve the ideal results.
A number of studies have shown that in the analysis of fMRI data, the rational use of the characteristics of fMRI data to introduce some reliable prior information will help to improve the performance of the method. The main objective of this paper is to use the general characteristics of the fMRI data, such as the non negative of data, the high dimensional structure characteristics and the spatial sparsity of the brain activation area. Non negative signal blind separation, tensor representation, and signal sparse representation and other signal processing frontiers, the algorithm framework based on convex analysis and convex optimization is established, and the reasonable prior information is introduced into the optimization process in convex constraint form, thus the calculation of fMRI data analysis and processing suitable for high dimension and large data is proposed. Methods the precise location of the brain activated area was realized and the neural decoding of higher education was performed.
The main work of this paper is as follows:
First, based on the sparse representation and tensor analysis, combined with the high dimensional characteristics of fMRI data, a regression model between fMRI data and task functions is established in tensor form. On this basis, two fMRI data analysis methods are proposed: a robust sparse voxel selection method based on multidimensional derivative constraints (Robust Voxel Selectio) N Method with Multi-dimensional Derivative Constraints, RVSMDC); the other is a robust neural decoding method based on multidimensional derivative constraints (Robust Sparse Decoding with Multi-dimensional). The spatial structure information of fMRI data is not destroyed, and it helps to improve the analysis of the data. The.RVSMDC method is proposed for the voxel selection analysis. At present, the traditional sparse representation method is too sparse to select the active voxel space, and it is difficult to form a mass (Cluster) in the analysis of the voxel selection. In this case, the RVSMDC method adds a multidimensional partial derivative constraint to the sparse representation optimization problem, so that the selected activator not only keeps the space sparsity, but also has the characteristics of the space block. In addition, we also introduce the error tolerance mechanism in the RVSMDC method to obtain the tolerance of the algorithm for the fMRI model error. The RSDMDC method is proposed for decoding analysis. In decoding analysis, the decoding accuracy is an important performance index. In order to obtain higher decoding accuracy, the RSDMDC method minimizes the regression error between the fMRI data and the task function in the optimized target function to obtain the regression coefficients that are most suitable for decoding analysis. The results show that the RSDMDC method can achieve higher decoding accuracy.
Secondly, on the basis of convex analysis, the blind separation method based on non negative and sparsity, the convex analysis method of Convex Analysis of Mixtures of Non-negative Sources, CAMNS, is introduced, and the continuous task correlation (Consist Task Related, CTR) components is selected from the decomposed components. In addition to the complex multi task parallel processing mechanism in the brain, the fMRI data contains a large number of unknown brain activity signals in addition to the brain functional signals that we are interested in. The traditional Blind Source Separation (BSS) method, the independent component analysis (Independent Component Analysis, ICA), is also included in the brain's complex multi task parallel processing mechanism. Depending on its powerful data mining ability, important progress has been made in the research of unknown brain activity patterns. However, recent studies have shown that the mathematical hypothesis of the independence of ICA method is difficult to be fully satisfied in the actual situation, resulting in the decline of the performance of the ICA algorithm for fMRI data analysis. In this paper, the CAMNS method mainly uses the fMRI signal book. The characteristics of the body, such as the non negativity of the signal, carry out blind decomposition. By means of the mathematical hypothesis of non negative and sparsity, the CAMNS method constructs a framework of convex analysis to estimate the source components. This process is achieved through two steps. First, the method shows that the source component can be geometrically regarded as a convex set. The convex set can be obtained by the observation data. Secondly, the process of estimating the source component can be considered as the process of determining the convex set endpoint built in the previous step. In addition, we use the separated CTR components to further the voxel selection and the neural decoding analysis. The experimental results show that the proposed algorithm can be obtained from the data. More useful information is excavated because it adopts mathematical assumptions that are more in line with the characteristics of fMRI data.
Finally, in order to make full use of the features of fMRI data to discover useful information hidden in fMRI data, we further explore how to convert more useful data features into reliable prior information and introduce the decomposition algorithm in convex constraints. For this reason, we propose a blind component method based on dictionary sparsity. The new method uses fMR. The characteristics of I data combine dictionary learning with sparse representation. Using the sparsity of the source component in the dictionary, the blind separation process is transferred to the sparse domain. Such measures can improve the quality of the blind separation. In the new method, the first need to select the appropriate dictionary according to the prior knowledge and use the pre selected dictionary. The blind separation process is transformed into a sparse domain, and then the sparse constraint of the source component in the sparse domain is used for blind decomposition. Choosing a suitable dictionary plays a key role in the performance of the proposed method. In order to extract the CTR fraction of interest from the fMRI data accurately, we need to select a suitable dictionary for the CTR In this paper, we choose the wavelet transform dictionary. By using a small fraction of the wavelet coefficients of the brain activation signal, we find that the wavelet transform can be used to sparse representation of the brain activation signals in the CTR component. The experimental results also show that the blind decomposition can be carried out in the sparse domain related to the CTR component. The accuracy of extracting CTR components is improved. Moreover, the CTR component based voxel selection and decoding analysis can also get better results.

【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：O174.13;R445.2

【参考文献】