Independent Component Analysis Involving Autocorrelated Sources With an Application to Functional Magnetic Resonance Imaging

• 成果类型: Article
• 署名作者: Lee, Seonjoo; Shen, Haipeng; Truong, Young; Lewis, Mechelle; Huang, Xuemei
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Penn State Health; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Penn State Health
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2011.tm10332
• 发表日期: 2011
• 页码: 1009-1024
• 关键词: blind separation; parkinsons-disease; fmri data; ica; time; algorithm; DECOMPOSITION; inference; mixture; signal

摘要

Independent component analysis (ICA) is an effective data-driven method for blind source separation. It has been successfully applied to separate source signals of interest from their mixtures. Most existing ICA procedures are carried out by relying solely on the estimation of the marginal density functions, either parametrically or nonparametrically. In many applications, correlation structures within each source also play an important role besides the marginal distributions. One important example is functional magnetic resonance imaging (fMRI) analysis where the brain-function-related signals are temporally correlated. In this article, we consider a novel approach to ICA that fully exploits the correlation structures within the source signals. Specifically, we propose to estimate the spectral density functions of the source signals instead of their marginal density functions. This is made possible by virtue of the intrinsic relationship between the (unobserved) sources and the (observed) mixed signals. Our methodology is described and implemented using spectral density functions from frequently used time series models such as autoregressive moving average (ARMA) processes. The time series parameters and the mixing matrix are estimated via maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through extensive simulation studies and a real fMRI application. The numerical results indicate that our approach outperforms several popular methods including the most widely used fastICA algorithm. This article has supplementary material online.