EPFL | Biomedical Imaging Group | Orthogonal Filterbanks

Statistical Analysis of fMRI Data Using Orthogonal Filterbanks

M. Feilner, T. Blu, M. Unser

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing VII, Denver CO, USA, July 19-23, 1999, vol. 3813, pp. 551–560.

Functional magnetic resonance imaging (fMRI) is a recent technique that allows the measurement of brain metabolism (local concentration of deoxyhemoglobin using BOLD contrast) while subjects are performing a specific task. A block paradigm produces alternating sequences of images (e.g., rest versus motor task). In order to detect and localize areas of cerebral activation, one analyzes the data using paired differences at the voxel level. As an alternative to the traditional approach which uses Gaussian spatial filtering to reduce measurement noise, we propose to analyze the data using an orthogonal filterbank. This procedure is intended to simplify and eventually imp ove the statistical analysis. The system is designed to concentrate the signal into a fewer number of components thereby improving the signal-to-noise ratio. Thanks to the orthogonality property, we can test the filtered components independently on a voxel-by-voxel basis; this testing procedure is optimal fo i.i.d. measurement noise. The number of components to test is also reduced because of down-sampling. This offers a straightforward approach to increasing the sensitivity of the analysis (lower detection threshold) while applying the standard Bonferroni correction fo multiple statistical tests. We present experimental results to illustrate the procedure. In addition, we discuss filter design issues. In particular, we introduce a family of orthogonal filters which are such that any integer reduction m can be implemented as a succession of elementary reductions m₁ to m_p where m = m₁ ... m_p is a prime number factorization of m.

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