EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > EPFL Thesis 2671


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Statistical Wavelet Analysis of Functional Images of the Brain

M.P. Feilner

Swiss Federal Institute of Technology Lausanne, EPFL Thesis no. 2671 (2002), 208 p., November 20, 2002.



feilner0201fig01

Functional magnetic resonance imaging (fMRI) is a recent, non-invasive technique that allows the measurement of brain metabolism while a subject is performing specific motor or cognitive tasks. The practical difficulty is that the signal changes are very small and the noise is relatively high. To enhance the activation signal, conventional methods, such as SPM, apply a Gaussian filter to the data and perform a statistical analysis at the pixel level. Gaussian filtering obviously suppresses high-frequency information. To avoid this loss of resolution, we propose instead to apply a wavelet transform and to perform the statistical analysis in the wavelet domain. Our statistical analysis relies on a conservative decision strategy which ensures that the false detection rate is kept well under control.

In the first chapter, we introduce the fMRI technique and compare it with other modalities. We then characterize the noise of fMRI data and introduce the statistical tools for our analysis. Next, we describe different types of wavelet transforms and show how those can be applied to the analysis of fMRI data.

Different wavelet bases offer different compromises. To determine the wavelet properties that are the most beneficial for the detection of activation patterns in fMRI data, we develop a test procedure for the objective evaluation of analysis methods. This procedure allows us to compare various brands of wavelet transforms, including Daubechies wavelets (real and complex) and the newly defined fractional splines. We observe that one of the transforms—dual fractional spline of degree 1.2—usually outperforms the others. We establish an interesting theoretical connection between this particular wavelet transform and the Gaussian filter recommended by SPM.

Traditional, separable wavelets are constrained to dyadic scale progressions (powers of two). To allow for finer scale progressions, we define new 2D and 3D fractional wavelets which use quincunx sampling. We propose an FFT-based implementation that turns out to be surprisingly fast. We also present some experimental examples where these quincunx wavelets offer some benefits.


@PHDTHESIS(http://bigwww.epfl.ch/publications/feilner0201.html,
AUTHOR="Feilner, M.P.",
TITLE="Statistical Wavelet Analysis of Functional Images of the
        Brain",
SCHOOL="{S}wiss {F}ederal {I}nstitute of {T}echnology {L}ausanne
        ({EPFL})",
YEAR="2002",
type="{EPFL} Thesis no.\ 2671 (2002), 208 p.",
address="",
month="November 20,",
note="")

© 2002 M.P. Feilner. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from M.P. Feilner.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.