Assessing self-similarity in redundant complex and quaternion wavelet domains: Theory and applications

dc.contributor.advisor Vidakovic, Brani
dc.contributor.author Kong, Tae Woon
dc.contributor.committeeMember Mei, Yajun
dc.contributor.committeeMember Paynabar, Kamran
dc.contributor.committeeMember Kang, Sung Ha
dc.contributor.committeeMember Lee, Kichun
dc.contributor.department Industrial and Systems Engineering
dc.date.accessioned 2019-05-29T14:02:49Z
dc.date.available 2019-05-29T14:02:49Z
dc.date.created 2019-05
dc.date.issued 2019-03-25
dc.date.submitted May 2019
dc.date.updated 2019-05-29T14:02:49Z
dc.description.abstract Theoretical self-similar processes have been an essential tool for modeling a wide range of real-world signals or images that describe phenomena in engineering, physics, medicine, biology, economics, geology, chemistry, and so on. However, it is often difficult for general modeling methods to quantify a self-similarity due to irregularities in the signals or images. Wavelet-based spectral tools have become standard solutions for such problems in signal and image processing and achieved outstanding performances in real applications. This thesis proposes three novel wavelet-based spectral tools to improve the assessment of self-similarity. First, we propose spectral tools based on non-decimated complex wavelet transforms implemented by their matrix formulation. A structural redundancy in non-decimated wavelets and a componential redundancy in complex wavelets act in a synergy when extracting wavelet-based informative descriptors. Next, we step into the quaternion domain and propose a matrix-formulation for non-decimated quaternion wavelet transforms and define spectral tools for use in machine learning tasks. We define non-decimated quaternion wavelet spectra based on the modulus and three phase-dependent statistics as low-dimensional summaries for 1-D signals or 2-D images. Finally, we suggest a dual wavelet spectra based on non-decimated wavelet transform in real, complex, and quaternion domains. This spectra is derived from a new perspective that draws on the link of energies of the signal with the temporal or spatial scales in the multiscale representations.
dc.description.degree Ph.D.
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/61244
dc.language.iso en_US
dc.publisher Georgia Institute of Technology
dc.subject Wavelets
dc.subject Classification
dc.subject Feature extraction
dc.title Assessing self-similarity in redundant complex and quaternion wavelet domains: 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
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