# The Statistical Analysis of Functional MRI DataBasis Function Approaches

The Statistical Analysis of Functional MRI Data: Basis Function Approaches The methods examined in this chapter have in common that they model the response of interest via some set of basis functions. The most popular approach by far is to use wavelets (Chui, 1992; Daubechies, 1992; Vidakovic, 1999). Wavelets have found a variety of applications in the fMRI literature and these are surveyed here together. Other basis functions, such as sets informed by anatomical considerations, and typical families such as splines, have also been explored by fMRI researchers, but in a much more limited capacity. Finally, polynomial and trigonometric basis functions are sometimes used as additional predictor variables in the general linear model. This chapter focuses on wavelets and anatomically informed basis func- tions. The former are of interest because they have wide applicability to fMRI data beyond being an extension of the basic linear model; indeed, wavelets have been used for creating activation maps, as a resampling technique, for data compression, and for modeling. The latter are of speciﬁc interest be- cause they represent attempts to directly use prior anatomical information, and hence to derive a set of functions that have intrinsic physiological mean- ing and interpretation (as opposed to trigonometric or spline functions, for example). 8.1 Wavelets http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# The Statistical Analysis of Functional MRI DataBasis Function Approaches

15 pages

/lp/springer-journals/the-statistical-analysis-of-functional-mri-data-basis-function-aUY9DE8htN
Publisher
Springer New York
ISBN
978-0-387-78190-7
Pages
1 –15
DOI
10.1007/978-0-387-78191-4_8
Publisher site
See Chapter on Publisher Site

### Abstract

The methods examined in this chapter have in common that they model the response of interest via some set of basis functions. The most popular approach by far is to use wavelets (Chui, 1992; Daubechies, 1992; Vidakovic, 1999). Wavelets have found a variety of applications in the fMRI literature and these are surveyed here together. Other basis functions, such as sets informed by anatomical considerations, and typical families such as splines, have also been explored by fMRI researchers, but in a much more limited capacity. Finally, polynomial and trigonometric basis functions are sometimes used as additional predictor variables in the general linear model. This chapter focuses on wavelets and anatomically informed basis func- tions. The former are of interest because they have wide applicability to fMRI data beyond being an extension of the basic linear model; indeed, wavelets have been used for creating activation maps, as a resampling technique, for data compression, and for modeling. The latter are of speciﬁc interest be- cause they represent attempts to directly use prior anatomical information, and hence to derive a set of functions that have intrinsic physiological mean- ing and interpretation (as opposed to trigonometric or spline functions, for example). 8.1 Wavelets

Published: Jun 7, 2008

Keywords: Basis Function; Receiver Operating Characteris Curve; fMRI Data; Wavelet Domain; Fractional Gaussian Noise