English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Wavelets have been shown to be effective bases for many classes of naturalsignals and images. Standard wavelet bases have the entire vector space$\mathbb R^n$ as their natural domain. It is fairly straightforward to adaptthese to rectangular subdomains, and there also exist constructions for domainswith more complex boundaries. However those methods are ineffective when wedeal with domains that are very arbitrary and convoluted. A particular exampleof interest is the human cortex, which is the part of the human brain where allthe cognitive activity takes place. In this thesis, we use the lifting schemeto design wavelets on arbitrary volumes, and in particular on volumes havingthe structure of the human cortex. These wavelets have an element of randomnessin their construction, which allows us to repeat the analysis with manydifferent realizations of the wavelet bases and averaging the results, a methodthat improves the power of the analysis. Next, we apply this type of wavelettransforms to the statistical analysis to fMRI data, and we show that itenables us to achieve greater spatial localization than other, more standardtechniques.

Randomized Wavelets on Arbitrary Domains and Applications to Functional MRI Analysis