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  本文選題：功能核磁共振成像 + 腦激活區(qū)定位�。� 參考：《華南理工大學》2014年博士論文

【摘要】：功能核磁共振成像(Functional Magnetic Resonance Imaging,fMRI)是一種重要的腦功能成像技術。它結合了功能、影像和解剖三方面的因素,是一種在活體人腦中定位腦功能區(qū)的有效方法。它具有諸多優(yōu)勢,如無創(chuàng)傷性、無放射性、較高的空間分辨率、可多次重復操作等。因此,fMRI技術已成為腦科學和生命科學研究中的重要工具。然而由于fMRI數據維數高,信噪比低,而且信號中混合了大量未知的腦活動模式,傳統(tǒng)處理方法往往難以達到理想效果。 多項研究表明,在fMRI數據的分析方法中,合理地利用fMRI數據的特點來引入一些可靠的先驗信息,將有助于提高方法的性能。本論文主要目標是根據fMRI數據的一般特性,如數據的非負性、高維結構特性和腦激活區(qū)的空間稀疏特性等,利用非負信號盲分離、張量表示、以及信號稀疏表示等信號處理領域的前沿方法,建立基于凸分析與凸優(yōu)化技術的算法框架,并將合理的先驗信息以凸約束形式引入優(yōu)化過程,從而提出高效的、適合高維大數據量的fMRI數據分析與處理的計算方法,實現(xiàn)對腦激活區(qū)的精確定位,并進行高教的神經解碼。 本論文的主要工作有以下幾個方面： 首先,以稀疏表示和張量分析為基礎,結合fMRI數據的高維性特點,以張量形式建立了fMRI數據和任務函數之間的回歸模型,并在此基礎上提出了兩種fMRI數據分析方法：一種是基于多維導數約束的魯棒稀疏體素選擇方法(Robust Voxel Selection Method with Multi-dimensional Derivative Constraints, RVSMDC);另一種是基于多維導數約束的魯棒神經解碼方法(Robust Sparse Decoding with Multi-dimensional Constraints, RSDMDC)。由于fMRI數據本身就是高階張量,利用張量技術來構建fMRI數據分析方法能夠很好地保持fMRI數據空間結構信息不被破壞,有助于提高算法對數據的分析能力。RVSMDC方法是針對體素選擇分析而提出的。目前傳統(tǒng)的稀疏表示方法在進行體素選擇分析時,存在選擇出的激活體素空間分布過于稀疏,較難形成團塊(Cluster)的問題。對此,RVSMDC方法在稀疏表示優(yōu)化問題中加入了多維偏導約束條件,以使得選擇出的激活體素不但保持空間稀疏特性,還同時具有空間團塊特點。此外,我們還在RVSMDC方法中引入了誤差容忍機制來獲取算法對fMRI模型誤差的容忍能力。RSDMDC方法是針對解碼分析而提出的。在解碼分析中,解碼準確率是一個重要的性能指標。為了獲取較高的解碼準確率,RSDMDC方法直接在優(yōu)化目標函數中最小化fMRI數據與任務函數之間的回歸誤差,來獲取最適合解碼分析的回歸系數。實驗結果表明,RSDMDC方法能夠取得較高的解碼準確率。 其次,以凸分析為基礎,引入了基于非負性和稀疏性的盲分離方法,即非負源混合觀測數據的凸分析方法(Convex Analysis of Mixtures of Non-negative Sources, CAMNS),并從分解得到分量中挑選出持續(xù)任務相關(Consist Task Related, CTR)分量來進一步進行體素選擇和解碼分析。由于大腦中復雜的多任務并行處理機制,fMRI數據中除了我們感興趣的腦功能活動信號之外,還包含了大量未知腦活動信號。傳統(tǒng)的盲分離(Blind Source Separation, BSS)方法,即獨立成分分析(Independent Component Analysis, ICA)依靠其強大的數據挖掘能力,在探索未知腦活動模式的研究中取得了重要進展。然而近期研究表明,ICA方法的獨立性數學假設在實際情況下很難完全滿足,導致ICA算法對于fMRI數據分析性能的下降。在本文中,CAMNS方法主要利用fMRI信號本身具有的特性,如信號的非負性,來進行盲分解。借助于非負性和稀疏性數學假設,CAMNS方法構建了一個凸分析的框架來對源分量進行估計。這個過程是通過兩個步驟來實現(xiàn)的。首先,該方法表明源分量在幾何上可以看作是一個凸集合的端點,該凸集合可以由觀測數據得到。其次,估計源分量的過程可以看作是確定上一步驟中所構建的凸集合端點的過程。此外,我們用分離得到的CTR分量進行進一步的體素選擇和神經解碼分析。實驗結果表明,所提出的算法能夠從數據中挖掘出更多有用信息,這是由于它采用了更符合fMRI數據特點的數學假設。 最后,為了充分利用fMRI數據特點來發(fā)掘隱藏在fMRI數據中的有用信息,我們進一步探索如何將更多有用的數據特點轉化為可靠的先驗信息,并以凸約束方式引入分解算法中。為此,我們提出了基于字典稀疏性的盲分量方法。新方法利用fMRI數據的特點,將字典學習和稀疏表示結合起來。利用源分量在字典中的稀疏性,來將盲分離的過程轉移到稀疏域中進行,這樣的措施能夠提高盲分離的質量。在新方法中,首先需要根據先驗知識選擇合適的字典,并利用預先選擇的字典來將盲分離過程變換到稀疏域中,然后再利用源分量在稀疏域中的稀疏性約束來進行盲分解。選擇一個合適的字典對于所提出方法的性能起著關鍵的作用。為了準確地從fMRI數據中提取出感興趣的CTR分量,我們需要選擇合適的字典來對CTR分量進行稀疏表示。在本文中,我們選擇了小波變換字典。通過將腦激活信號用一小部分小波系數來表示,我們發(fā)現(xiàn)小波變換可以較好地對CTR分量中的腦激活信號進行稀疏表示。實驗結果也表明,在CTR分量相關的稀疏域中進行盲分解能夠提高提取CTR分量的準確性。此外,基于CTR分量的體素選擇和解碼分析也能夠得到較好的結果。
[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.

【學位授予單位】：華南理工大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：O174.13;R445.2

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