Will Chang

Harvey Mudd College Mathematics 2004

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Thesis Proposal: Representation Theoretical Methods in Image Processing
Thesis Advisor: Prof. Michael Orrison
Second Reader: Prof. Weiqing Gu
E-Mail: wchang@math.hmc.edu
Final Draft: Final Thesis

Image Processing with Wreath Products

We present a technique to decompose digital images using generalizations of the Discrete Fourier Transform (DFT). This method arises from the representation theory of iterated wreath product groups, which describe symmetries of the quad tree decomposition of an image. In addition, we describe applications to compression, edge detection, and de-noising, as well as experimental results to evaluate the performance of these operations.