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On Multi-Scale Refinement of Discrete Data

<p> It is possible to interpret multi-resolution analysis from both Fourier-domain and temporal/spatial domain stand-points. While a Fourier-domain interpretation helps in designing a powerful machinery for multi-resolution refinement on regular point-sets and lattices, most of its techniques cannot be directly generalized to the case of irregular sampling. Therefore, in this thesis we provide a new definition and formulation of multi-resolution refinement, based on a temporal/spatial-domain understanding, that is general enough to allow multi-resolution approximation of different spaces of functions by processing samples (or observations) that can be irregularly distributed or even obtained using different sampling methods. We then continue to provide a construction for designing and implementing classes of refinement schemes in these general settings. The framework for multi-resolution refinement that we discuss includes and extends the existing mathematical machinery for multi-resolution analysis; and the suggested construction unifies many of the schemes currently in use, and, more importantly, allows designing schemes for many new settings. </p> / Thesis / Master of Applied Science (MASc)

Identiferoai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/21863
Date10 1900
CreatorsDehghani Tafti, Pouya
ContributorsShirani, S., Wu, X., None
Source SetsMcMaster University
LanguageEnglish
Detected LanguageEnglish

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