07_Wavelet

07_Wavelet - Surfing the Brain FUNCTIONAL MAGNETIC...

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IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006 65 FUNCTIONAL MAGNETIC RESONANCE IMAGING Surfing the Brain An Overview of Wavelet-Based Techniques for fMRI Data Analysis BY DIMITRI VAN DE VILLE, THIERRY BLU, AND MICHAEL UNSER ©DIGITAL STOCK 0739-5175/06/$20.00©2006IEEE T he measurement of brain activity in a noninvasive way is an essential element in modern neurosciences. Modalities such as electroencephalography (EEG) and magnetoencephalography (MEG) recently gained inter- est, but two classical techniques remain predominant. One of them is positron emission tomography (PET), which is costly and lacks temporal resolution but allows the design of tracers for specific tasks; the other main one is functional magnetic resonance imaging (fMRI), which is more affordable than PET from a technical, financial, and ethical point of view, but which suffers from poor contrast and low signal-to-noise ratio (SNR). For this reason, advanced methods have been devised to perform the statistical analysis of fMRI data. The blood-oxygen-level-dependent (BOLD) signal, discov- ered by [1] in the 1990s and later elucidated in [2], has allowed fMRI to evolve into a prominent tool to perform non- invasive studies of the function of the brain. In T2*-weighted magnetic resonance (MR) images, the BOLD signal exhibits a weak and noisy contrast. The aim of fMRI data analysis is to detect this signal in a time series of acquisitions. The purpose of this article is to give a unifying overview of techniques that deploy the wavelet transform to perform this analysis. The wavelet transform is a powerful tool [3], [4]. Unlike the Fourier sinusoids, which provide a sharp frequency characteri- zation of a given signal but are unable to identify transient events, wavelets achieve a balance between localization in space or time and localization in the frequency domain. This balance is intrinsic to multiresolution, which allows the analy- sis to deal with image features at any scale. As the discrete wavelet transform (DWT) corresponds to a basis decomposi- tion, it provides a nonredundant and unique representation of the signal. These fundamental properties are key to the effi- cient decomposition of the nonstationary processes typical of fMRI experimental settings. Consequently, wavelets have received a large recognition in biomedical signal and image processing; several overviews are available [5]–[7], including work that is tailored to fMRI [8]. The first application of wavelets in fMRI was pioneered by Ruttimann et al. [9], [10]. After computing the wavelet trans- form of each volume, the parameter for an on/off type activa- tion is extracted, followed by a coefficient-wise statistical test for this parameter. Such a procedure takes advantage of two properties of the wavelet transform. First, wavelets allow us to obtain a sparse representation of the activation map, in the sense that only a few wavelet coefficients are needed to effi- ciently encode the spatial activation patterns. Consequently, the SNR of signal-carrying coefficients has increased with
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07_Wavelet - Surfing the Brain FUNCTIONAL MAGNETIC...

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