Title:
Non-decimated wavelet transform in statistical assessment of scaling: Theory and applications
Non-decimated wavelet transform in statistical assessment of scaling: Theory and applications
dc.contributor.advisor | Vidakovic, Brani | |
dc.contributor.author | Kang, Min Kyoung | |
dc.contributor.committeeMember | Goldsman, David | |
dc.contributor.committeeMember | Haaland, Ben | |
dc.contributor.committeeMember | Paynabar, Kamran | |
dc.contributor.committeeMember | Voit, Eberhard O. | |
dc.contributor.department | Industrial and Systems Engineering | |
dc.date.accessioned | 2016-08-22T12:22:05Z | |
dc.date.available | 2016-08-22T12:22:05Z | |
dc.date.created | 2016-08 | |
dc.date.issued | 2016-05-13 | |
dc.date.submitted | August 2016 | |
dc.date.updated | 2016-08-22T12:22:05Z | |
dc.description.abstract | In this thesis, we introduced four novel methods that facilitate the scaling estimation based on NDWT. Chapter 2 introduced an NDWT matrix which is used to perform an NDWT in one or two dimensions. The use of matrix significantly decreased the computation time when 2-D inputs of moderate size are transformed under MATLAB environment, and such reduction of computation time was augmented when the same type of NDWT is performed repeatedly. With 2-D inputs, an NDWT matrix yielded a scale-mixing NDWT, which is more compressive than the standard 2-D NDWT. The retrieval of an original signal after the transform was possible with a weight matrix. An NDWT matrix can handle signals of non-dyadic sizes in one or two dimensions. The proposed NDWT matrix was used for the transforms in Chapters 3-5. Chapter 3 introduced a method for scaling estimation based on a non-decimated wavelet spectrum. A distinctive feature of NDWT, redundancy, enables us to obtain local spectra and improves the accuracy of scaling estimation. For simulated signals with known $H$ values, the method yields estimators of $H$ with lower mean squared errors. We characterized mammographic images with the proposed scaling estimator and anisotropy measures from non-decimated wavelet spectra for breast cancer detection, and obtained the best diagnostic accuracy in excess of 80\%. Some real-life signals are known to possess a theoretical value of the Hurst exponent. Chapter 4 described a Bayesian scaling estimation method that utilizes the value of a theoretical scaling index as a mean of prior distribution and estimates $H$ with MAP estimation. The accuracy of estimators from the proposed method is robust to small misspecification of the prior mean. We applied the method to a turbulence velocity signal and yielded an estimator of $H$ close to the theoretical value. Chapter 5 proposed two methods based on NDWT for robust estimation of Hurst exponent $H$ of 1-D self-similar signals. The redundancy of NDWT, which improved the accuracy of estimation, introduced autocorrelations within the wavelet coefficients. With the two proposed methods, we alleviated the autocorrelation in three ways: taking the logarithm prior to taking the median, relating Hurst exponent to the median instead of mean of the model distribution, and resampling the coefficients. | |
dc.description.degree | Ph.D. | |
dc.format.mimetype | application/pdf | |
dc.identifier.uri | http://hdl.handle.net/1853/55579 | |
dc.language.iso | en_US | |
dc.publisher | Georgia Institute of Technology | |
dc.subject | Non-decimated wavelet transform | |
dc.subject | Scaling | |
dc.subject | Hurst exponent | |
dc.title | Non-decimated wavelet transform in statistical assessment of scaling: Theory and applications | |
dc.type | Text | |
dc.type.genre | Dissertation | |
dspace.entity.type | Publication | |
local.contributor.advisor | Vidakovic, Brani | |
local.contributor.corporatename | H. Milton Stewart School of Industrial and Systems Engineering | |
local.contributor.corporatename | College of Engineering | |
relation.isAdvisorOfPublication | 1463fd97-3d52-4269-afac-97f6f7f46fcd | |
relation.isOrgUnitOfPublication | 29ad75f0-242d-49a7-9b3d-0ac88893323c | |
relation.isOrgUnitOfPublication | 7c022d60-21d5-497c-b552-95e489a06569 | |
thesis.degree.level | Doctoral |