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Authors: Ozkaya, Gorkem G
Advisors: Daubechies, Ingrid C
Contributors: Applied and Computational Mathematics Department
Keywords: fMRI
Lifting scheme
statistical analysis
Wavelet design
Subjects: Mathematics
Electrical engineering
Issue Date: 2012
Publisher: Princeton, NJ : Princeton University
Abstract: Wavelets have been shown to be effective bases for many classes of natural signals and images. Standard wavelet bases have the entire vector space <bold>R</bold><super>n</super> as their natural domain. It is fairly straightforward to adapt these to rectangular subdomains, and there also exist constructions for domains with more complex boundaries. However those methods are ineffective when we deal with domains that are very arbitrary and convoluted. A particular example of interest is the human cortex, which is the part of the human brain where all the cognitive activity takes place. In this thesis, we use the lifting scheme to design wavelets on arbitrary volumes, and in particular on volumes having the structure of the human cortex. These wavelets have an element of randomness in their construction, which allows us to repeat the analysis with many different realizations of the wavelet bases and averaging the results, a method that improves the power of the analysis. Next, we apply this type of wavelet transforms to the statistical analysis to fMRI data, and we show that it enables us to achieve greater spatial localization than other, more standard techniques.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Applied and Computational Mathematics

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