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首页> 外文学位 >Novel wavelet-based statistical methods with applications in classification, shrinkage, and nano-scale image analysis.
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Novel wavelet-based statistical methods with applications in classification, shrinkage, and nano-scale image analysis.

机译：基于小波的新型统计方法，可应用于分类，收缩和纳米级图像分析。

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摘要

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: (1) 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. (2) 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 the local False Discovery Rate (FDR), Bayes factors and ordering of posterior probabilities. (3) 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.
机译：鉴于小波变换最近的流行和广泛应用的明确证据，本论文致力于小波变换的几种统计应用。在最近的十年中，统计多尺度建模已成为理论和应用统计领域中公认的领域，对统计方法的发展产生了影响。基于小波的方法在诸如回归，密度和函数估计，因子分析，时间序列分析中的建模和预测，评估数据的自相似性和分形性以及空间统计等领域的统计中非常重要。本文通过考虑三个问题来证明小波的适用性：（1）考虑基于二进制小波的线性分类器。一致性结果和实施问题都得到解决。我们表明，在温和的假设下，基于小波的分类规则既弱又普遍一致。在已知“真相”的合成数据集以及来自工业和生物工程领域的应用分类问题上，说明了所提出的方法。 （2）我们在检验小波域中的多个假设的基础上开发了小波收缩方法。通过许多假设的隐式或显式同时检验的收缩/阈值方法已被许多研究人员考虑，并且可以追溯到1990年代初。我们基于局部错误发现率（FDR），贝叶斯因子和后验概率排序，提出了两种新的小波收缩/阈值处理方法。 （3）提出了一种新的基于霍夫和小波变换的图像特征直线对齐分析方法。该新方法旨在与纳米尺度的透射电子显微镜（TEM）图像配合使用，以检测由原子晶格形成的线性结构。

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  • 作者

    Lavrik, Ilya.;

  • 作者单位

    Georgia Institute of Technology.;

  • 授予单位 Georgia Institute of Technology.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2006
  • 页码 135 p.
  • 总页数 135
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 统计学;
  • 关键词

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