Application of Polynomial Spline Independent Component Analysis to fMRI Data

Kawaguchi, Atsushı; Truong, Young K.; Huang, Xuemei

doi:10.5772/50343

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…Among the several useful measures for evaluating BSS algorithms, one of the most used is (Amari metric), proposed by Amari (KAWAGUCHI et al 2012). It compares the elements of = 0 −1 0 , with the th column of given by .…”

Section: Performance Measuresmentioning

confidence: 99%

Blind Source Separation by Multiresolution Analysis using AMUSE Algorithm

Oliveira

Duarte

Filho

2018

MSJ

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Algorithms for blind source separation have been extensively studied in the last years. This paper proposes the use of multiresolution analysis in three decomposition levels of the wavelet transform, such as a preprocessing step, and the AMUSE algorithm to separate the source signals in distinct levels of resolution. Results show that there is an improvement in the estimation of the signals and in the mixing matrix even in noisy environment if compared to the use of AMUSE only.

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Section: Performance Measuresmentioning

confidence: 99%

Blind Source Separation by Multiresolution Analysis using AMUSE Algorithm

Oliveira

Duarte

Filho

2018

MSJ

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“…More flexible nonparametric methods include estimating the score function using kernel approximation (Vlassis and Motomura 2001), kernel density estimation (Bach and Jordan 2003; Boscolo, Pan, and Roychowdhury 2004; Chen and Bickel 2005; Chen 2006; Shen, Hüper, and Smola 2006), smoothing splines (Hastie and Tibshirani 2003), B -spline approximation (Chen and Bickel 2006), and logsplines (Kawaguchi and Truong 2009). Two other relaxations of the basic ICA model are subspace ICA (Hyvärinen and Hoyer 2000; Sharma and Paliwal 2006) that allows the sources to form mutually independent subgroups and does not require the sources within the same subgroup to be independent; and AMICA (Palmer et al 2008) that uses mixtures of Gaussian scale mixtures to model the sources, which was extended to include mixtures of linear processes (Palmer, Kreutz-Delgado, and Makeig 2010).…”

Section: Introductionmentioning

confidence: 99%

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

Lee

Shen

Truong

et al. 2011

Journal of the American Statistical Association

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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.

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