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.

Cyber criminals are trying to steal personal information from victim¡¦s machine to acquire more benefits by using malware. Antivirus is the most commonly used tool of malware identification, but the frequency of virus definition update is often less than the frequency of new type malware increase. Therefore, we need an effective and fast tool of malware identification in the current environment. In addition to antivirus, software analysis platform is currently one of the ways to identify malware. User could figure out behaviors of software in detail by the analysis report provided by software analysis platform. Most of software analysis platforms only offer an analysis report, user have to identify whether the software is malware or not by them self. This type of report is no help for user if their expertise not enough to find out these behaviors. Some of software analysis platforms which used antivirus can provide information to user about the software is malware or not, but they don¡¦t have the ability of identifying new type malware immediately. According to research and analysis report, we generalized differences in file and registry activities of normal software and malware and defined malware classification features from these differences. We adopted Support Vector Machine¡]SVM¡^as our algorithm of classification to build and test three classifiers which can identify normal software and malware. After several experimental evaluations, we confirmed that the identification rate of malware was up to 97.6%. Finally, we compared the performance of our classifiers with ThreatExpert, and the result show that the performance of our classifiers is as well as ThreatExpert.

名古屋大学博士学位論文 学位の種類 : 博士(医学)(課程) 学位授与年月日:平成23年3月31日 申正樹氏の博士論文として提出された

Thèse doctorat : Informatique : Villeurbanne, INSA : 2006. / Thèse entièrement rédigée en anglais. Titre provenant de l'écran-titre. Bibliogr. p. 141-157.

Thèse de doctorat : Sciences informatiques : Paris 12 : 2007. / Thèse uniquement consultable au sein de l'Université Paris 12 (Intranet). Titre provenant de l'écran-titre. Bibliogr. : 77 réf.

Reproduction de : Thèse doctorat : Informatique : Avignon : 2000. / Titre provenant de l'écran-titre. Bibliogr. p. 159-176.

Reproduction de : Thèse doctorat : Informatique : Metz : 2003. / Titre provenant de l'écran-titre. Notes bibliographiques.

Thèse doctorat : Informatique : Strasbourg 1 : 2006. / Titre provenant de l'écran-titre. Bibliogr. 10 p.

Ph.d.

Thesis (M. Phil.)--University of Hong Kong, 1989.