基于凸分析的盲分解方法及在脑功能磁共振成像数据分析中的应用

摘要

盲分解(blind source separation,BSS)是经典的功能磁共振成像(functional magnetic resonance imaging,fMRI)数据驱动类分析方法.独立成分分析(independent component analysis,ICA)是fMRI数据盲分解的常用方法之一,主要利用源分量的独立性假设来从fMRI数据中提取持续任务相关(consistent task related,CTR)成分.然而在实际fMRI数据处理中发现源分量的独立性假设很难完全满足.为了提高CTR成分提取准确率,利用CTR分量空间稀疏性特点,引入基于凸分析的盲分解技术来分析fMRI数据.新方法包含两个步骤,首先利用fMRI观测数据构建一个凸集合,将源分量定位问题转化为在几何上确定凸集合端点;其次,通过体积最大法来确定凸集合端点.数值结果表明该方法可以从fMRI数据中提取更多有用信息,提高了CTR分量获取的准确率,有利于定位与任务相关的脑激活区.%Functional magnetic resonance imaging(fMRI)data analysis is of great challenge for its characteristics of high dimensionality and low signal noise ratio.Independent component analysis(ICA)is a classical approach for analysis of fMRI data.ICA based methods exploit independence assumption while extracting consistent task related(CTR)component from fMRI data. However,recent studies show that independence assumption of ICA based method is sometime violated in practice due to the principle of"functional integration"of human brain. In this paper,we proposed a new fMRI data analysis method based on blind source separation(BSS)technique.The proposed method does not emphasize independence assumption but sparsity and non-negativity,which is considered more realistic to fMRI data.With convex optimization,we constructed a closed convex set on the observed fMRI data.Then,the task of estimating the source component is converted into the task of geometrically determining the extreme points of the convex set. While determining the extreme points, alternative volume maximum(AVM)is used to find a simplex with maximum volume to approximate the obtained convex set to achieve robustness against fMRI modelling errors. Numerical results in this paper show that proposed method may localize brain activations with higher accuracy rate.