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Characterizing the functional MRI response using Tikhonov regularization
Author(s) -
Vakorin Vasily A.,
Borowsky Ron,
Sarty Gordon E.
Publication year - 2007
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2981
Subject(s) - tikhonov regularization , regularization (linguistics) , computer science , artificial intelligence , mathematics , inverse problem , mathematical analysis
The problem of evaluating an averaged functional magnetic resonance imaging (fMRI) response for repeated block design experiments was considered within a semiparametric regression model with autocorrelated residuals. We applied functional data analysis (FDA) techniques that use a least‐squares fitting of B‐spline expansions with Tikhonov regularization. To deal with the noise autocorrelation, we proposed a regularization parameter selection method based on the idea of combining temporal smoothing with residual whitening. A criterion based on a generalized χ 2 ‐test of the residuals for white noise was compared with a generalized cross‐validation scheme. We evaluated and compared the performance of the two criteria, based on their effect on the quality of the fMRI response. Wefound that the regularization parameter can be tuned to improve the noise autocorrelation structure, but the whitening criterion provides too much smoothing when compared with the cross‐validation criterion. The ultimate goal of the proposed smoothing techniques is to facilitate the extraction of temporal features in the hemodynamic response for further analysis. In particular, these FDA methods allow us to compute derivatives and integrals of the fMRI signal so that fMRI data may be correlated with behavioral and physiological models. For example, positive and negative hemodynamic responses may be easily and robustly identified on the basis of the first derivative at an early time point in the response. Ultimately, these methods allow us to verify previously reported correlations between the hemodynamic response and the behavioral measures of accuracy and reaction time, showing the potential to recover new information from fMRI data. Copyright © 2007 John Wiley & Sons, Ltd.

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