Thesis Defense :: Novel Wavelet-Based Statistical Methods with Applications in Classification, Shrinkage, and Nano-Scale Image Analysis

Event Details
  • Date/Time:
    • Monday November 14, 2005 - Sunday November 13, 2005
      9:00 am - 11:00 pm
  • Location: ISyE 226A Groseclose Buliding
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Contact
Barbara Christopher
Industrial and Systems Engineering
Contact Barbara Christopher
404.385.3102
Summaries

Summary Sentence: Thesis Defense :: Novel Wavelet-Based Statistical Methods with Applications in Classification, Shrinkage, and Nano-Scale Image Analysis

Full Summary: Thesis Defense :: Novel Wavelet-Based Statistical Methods with Applications in Classification, Shrinkage, and Nano-Scale Image Analysis

Given the recent popularity and clear evidence of wide applicability of wavelets, this thesis is devoted to several statistical applications of Wavelet transforms. Statistical multiscale modeling has, in the most recent decade, become a well established area in both theoretical and applied statistics, with impact on developments in statistical methodology.

Wavelet-based methods are important in statistics in areas such as regression, density and function estimation, factor analysis, modeling and forecasting in time series analysis, assessing self-similarity and fractality in data, and spatial statistics. In this thesis we show applicability of the wavelets by considering three problems:

First, we consider a binary wavelet-based linear classifier. Both consistency results and implemental issues are addressed. We show that under mild assumptions wavelet-based classification rule is both weakly and strongly universally consistent. The proposed method is illustrated on synthetic data sets in which the "truth" is known and on applied classification problems from the industrial and bioengineering fields.

Second, we develop wavelet shrinkage methodology based on testing multiple hypotheses in the wavelet domain. The shrinkage/thresholding approach by implicit or explicit simultaneous testing of many hypotheses had been considered by many researchers and goes back to the early 1990's. We propose two new approaches to wavelet shrinkage/thresholding based on local False Discovery Rate (FDR), Bayes factors and ordering of posterior probabilities.

Finally, we propose a novel method for the analysis of straight-line alignment of features in the images based on Hough and Wavelet transforms. The new method is designed to work specifically with Transmission Electron Microscope (TEM) images taken at nanoscale to detect linear structure formed by the atomic lattice.

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H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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Status
  • Created By: Barbara Christopher
  • Workflow Status: Published
  • Created On: Oct 8, 2010 - 7:37am
  • Last Updated: Oct 7, 2016 - 9:52pm