Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/21863
Title: | On Multi-Scale Refinement of Discrete Data |
Authors: | Dehghani Tafti, Pouya |
Advisor: | Shirani, S. Wu, X. |
Department: | None |
Keywords: | Discrete Data;Refinement;Multi-Scale;multi-resolution analysis |
Publication Date: | Oct-2005 |
Abstract: | <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> |
URI: | http://hdl.handle.net/11375/21863 |
Appears in Collections: | Digitized Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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DehghaniTafti_Pouya_2005Oct_Masters.pdf | 3.85 MB | Adobe PDF | View/Open |
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