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27 September 2007 Activelets and sparsity: a new way to detect brain activation from fMRI data
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FMRI time course processing is traditionally performed using linear regression followed by statistical hypothesis testing. While this analysis method is robust against noise, it relies strongly on the signal model. In this paper, we propose a non-parametric framework that is based on two main ideas. First, we introduce a problem-specific type of wavelet basis, for which we coin the term "activelets". The design of these wavelets is inspired by the form of the canonical hemodynamic response function. Second, we take advantage of sparsity-pursuing search techniques to find the most compact representation for the BOLD signal under investigation. The non-linear optimization allows to overcome the sensitivity-specificity trade-off that limits most standard techniques. Remarkably, the activelet framework does not require the knowledge of stimulus onset times; this property can be exploited to answer to new questions in neuroscience.
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Ildar Khalidov, Dimitri Van De Ville, Jalal Fadili, and Michael Unser "Activelets and sparsity: a new way to detect brain activation from fMRI data", Proc. SPIE 6701, Wavelets XII, 67010Y (27 September 2007); doi: 10.1117/12.734706;

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