Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01s1784k77x
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dc.contributor.authorOzkaya, Gorkem Gen_US
dc.contributor.otherApplied and Computational Mathematics Departmenten_US
dc.date.accessioned2012-11-15T23:54:25Z-
dc.date.available2012-11-15T23:54:25Z-
dc.date.issued2012en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01s1784k77x-
dc.description.abstractWavelets 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.en_US
dc.language.isoenen_US
dc.publisherPrinceton, NJ : Princeton Universityen_US
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the <a href=http://catalog.princeton.edu> library's main catalog </a>en_US
dc.subjectfMRIen_US
dc.subjectLifting schemeen_US
dc.subjectstatistical analysisen_US
dc.subjectWavelet designen_US
dc.subject.classificationMathematicsen_US
dc.subject.classificationElectrical engineeringen_US
dc.titleRANDOMIZED WAVELETS ON ARBITRARY DOMAINS AND APPLICATIONS TO FUNCTIONAL MRI ANALYSISen_US