Methods For FMEI Data Analysis Based On Convex Analysis And Optimization

Functional magnetic resonance imaging (fMRI) is an important technique for brainfunction imaging. It takes three elements into consideration such as function, image, andanatomy. It is an effective approach to localize brain functional areas in the living body.fMRI technique has plenty of advantages such as non-invasive, non-radioactive, hightemporal and spatial resolution and multi-repeat operation as well. Therefore, fMRI hasalready become an important research tool in brain science and life science. However,due to characteristics of high dimensionality, low signal-to-noise ratio and containing alarge number of unknown patterns of brain activities, the traditional methods are oftendiiffcult to get satisfactory results.Several studies have shown that exploiting some reasonable prior information offMRI data is helpful for improving performance of fMRI data analysis methods. Themain goal of this study is to use some new techniques in signal processing ifelds, e.g., non-negative blind signal separation, tensor formulation, sparse representation to establish theconvex analysis and optimization based framework. The new framework makes full useof general characteristics of fMRI data, e.g.，non-negativity, high dimensionality, sparsity.By introducing the general characteristics of fMRI data as reasonable convex constraintsinto optimization problem, the proposed methods is more suitable for analyzing fMRIdata and can achieve higher performance on voxel selection and neural decoding analysis.The main contributions of this dissertation are summarized as follows:First, considering high dimension dimensionality of fMRI data, a regression modelbetween fMRI data and task function is established by using tenor formulation and sparserepresentation. Moreover, two new methods are proposed based on the proposed regres?sion model, one is robust voxel selection with multi-dimensional constraint (RVSMDC),the other one is robust sparse decoding with multi-dimensional constraints (RSDMDC).For fMRI data are naturally tensor objects, it is found that using tensor formulationwill not destroy the natural structure of fMRI data. Thus, using tensor formulation ishelpful for improving performance of data analysis methods. The RVSMDC is proposedfor voxel selection. It is found that voxels selected by conventional sparse representationmethods are ’too sparse’ in spatial distribution and hardly show clustering effect. In or?der to overcome this problem, the RVSMDC based method introduces multi-dimensional derivative constraints into optimization problem of sparse representation to make selectedvoxels achieve sparse spatial distribution and clustering effects. Moreover, by introducinga error tolerance mechanism, the RVSMDC is able to tolerate some modeling error. TheRSDMDC is proposed for decoding analysis. For decoding analysis, decoding accuracy isan important performance indicator. In order to achieve higher decoding accuracy, theRSDMDC directly minimizes the regression error of fMRI data to the task function toobtain suitable regression coeiffcients for decoding analysis. Moreover, numerical resultsshow that the RSDMDC can achieve higher decoding accuracy.Second, we introduce a new blind source separation (BSS) method, based on convexanalysis of mixtures of non-negative sources (CAMNS) technique, for fMRI componentsanalysis and apply the separated consist task related (CTR) components in voxel se?lection and neural decoding processes. Due to complicated multi-task mechanisms inbrain, fMRI data contains a lot of unknown patterns of brain activity in addition tothe interested signal of brain function. The conventional blind source separation (BSS)method, independent component analysis (ICA) has made great contribution in exploringunknown patterns of brain activity with its strong data mining ability. However, recentstudy show that the independence assumption of ICA based method may be violatedin practice. This may results in performance degradation. In this work, CAMNS basedmethod does not require independence assumption but to exploit some general charac?teristic of fMRI data, e.g., non-negativity, to blindly decompose fMRI data. Based onnon-negativity and sparsity assumptions, the new BSS method estimates the source com?ponents in a convex analysis framework. It is achieved in two steps. First, it shows thatsource components serve as extreme points of a convex set, which is constructed basedon the observed fMRI data. Next, all the source components can be estimated by ifndingextreme points of the convex set obtained in the first step. Moreover, voxel selectionand neural decoding methods based on blind separated CTR source components are alsopresented in this work. Numerical results show that the proposed method can extractmore useful information from fMRI data. This advantage may be obtained by the factthat the proposed method exploits mathematical assumptions considered more realisticto fMRI data.Last, to make full use of characteristics of fMRI data to mine useful informationhiding in fMRI data, we further explore how to introduce more useful prior informationaccording to characteristics of fMRI data as convex constraints into optimization problemof separation algorithms. To do this, we proposed a new BSS method, which combinesdictionary learning and sparse representation. By exploiting sparsity of source componentin a signal dictionary, the blind separation process is converted to the transformed sparsedomain. Estimating source component in the sparse domain is helpful for improving quality of blind separation equality. In the proposed method, we should first select aproper dictionary by prior information. Then, the blind separation process is performedin the transformed domain. The source components is estimated by imposing sparsityconstraint in the transformed domain. Note that selecting a proper dictionary plays akey role for the performance of the proposed method. To extract consist task related(CTR) components from fMRI data, it is important to ifnd a dictionary to sparsify theactivation signals in CTR components. In this paper, we recommend wavelet transform asa candidate dictionary. Several studies show that activation signals in CTR componentscan be well sparsiifed by being represented with a small number of wavelet coefifcients.Numerical results show that performing blind separation process in the CTR componentrelated sparse domain is helpful for improving accuracy of CTR components estimation.Moreover, higher performance on voxel selection and neural decoding can be achieved byusing the separated CTR components.