Likelihood-based hypothesis tests for brain activation detection from MRI data disturbed by colored noise: A simulation study

A. J. Den Dekker, D. H.J. Poot, R. Bos, J. Sijbers

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14 Citations (Scopus)


Functional magnetic resonance imaging (fMRI) data that are corrupted by temporally colored noise are generally preprocessed (i.e., prewhitened or precolored) prior to functional activation detection. In this paper, we propose likelihood-based hypothesis tests that account for colored noise directly within the framework of functional activation detection. Three likelihood-based tests are proposed: the generalized likelihood ratio (GLR) test, the Wald test, and the Rao test. The fMRI time series is modeled as a linear regression model, where one regressor describes the task-related hemodynamic response, one regressor accounts for a constant baseline and one regressor describes potential drift. The temporal correlation structure of the noise is modeled as an autoregressive (AR) model. The order of the AR model is determined from practical null data sets using Akaike's information criterion (with penalty factor 3) as order selection criterion. The tests proposed are based on exact expressions for the likelihood function of the data. Using Monte Carlo simulation experiments, the performance of the proposed tests is evaluated in terms of detection rate and false alarm rate properties and compared to the current general linear model (GLM) test, which estimates the coloring of the noise in a separate step. Results show that theoretical asymptotic distributions of the GLM, GLR, and Wald test statistics cannot be reliably used for computing thresholds for activation detection from finite length time series. Furthermore, it is shown that, for a fixed false alarm rate, the detection rate of the proposed GLR test statistic is slightly, but (statistically) significantly improved compared to that of the common GLM-based tests. Finally, simulations results reveal that all tests considered show seriously inferior performance if the order of the AR model is not chosen sufficiently high to give an adequate description of the correlation structure of the noise, whereas the effects of (slightly) overmodeling are observed to be less harmful.

Original languageEnglish
Article number4601459
Pages (from-to)287-296
Number of pages10
JournalIEEE Transactions on Medical Imaging
Issue number2
Publication statusPublished - Feb 2009
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received May 22, 2008; revised July 24, 2008. First published August 15, 2008; current version published January 30, 2009. This work was supported in part by the FWO (Fund for Scientific Research—Belgium) and in part by I.W.T. (Institute for Science and Technology—Belgium). Asterisk indicates corresponding authors. *A. J. den Dekker is with the Delft University of Technology, Delft Center for Systems and Control, 2828 CD Delft, The Netherlands (e-mail:


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