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