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http://hdl.handle.net/1903/9586
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| Title: | Enumeration of Harmonic Frames and Frame Based Dimension Reduction |
| Authors: | Hirn, Matthew John |
| Advisors: | Benedetto, John J
Okoudjou, Kasso A |
| Department/Program: | Mathematics |
| Type: | Dissertation |
| Sponsors: | Digital Repository at the University of Maryland
University of Maryland (College Park, Md.) |
| Keywords: | 0405
Mathematics
dimension reduction, frames, harmonic frames, hyperspectral imagery data, kernel eigenmap methods |
| Issue Date: | 2009 |
| Abstract: | We investigate two aspects of frame theory, one of a theoretical
nature, the other very much on the applied side. In the former, we
enumerate all harmonic frames of prime order, and develop partial
proofs concerning the structure of the symmetry group for this subset
of frames. In the latter, we develop frame theory in the context of
kernel eigenmap methods, merging the two theories in a practical
manner and applying new algorithms to hyperspectral imagery data for
the purposes of material classification. These two problems, while
seemingly separate, are united by frame theory and serve to illustrate
both the beautiful theoretical nature of frames as well as their
practicality in dealing with real world problems. |
| URI: | http://hdl.handle.net/1903/9586 |
| Appears in Collections: | UMD Theses and Dissertations
Mathematics Theses and Dissertations
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