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

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.

Level thesis:degree_level

Doctoral

Department dc:contributor.department

Industrial and Systems Engineering

Grantor dc:publisher

Georgia Institute of Technology

Year dc:date.issued

2019

Author dc:creator

• Kong, Tae Woon

Advisor dc:contributor.advisor

• Vidakovic, Brani

Committee members dc:contributor.committeemember

• Mei, Yajun
• Paynabar, Kamran
• Kang, Sung Ha
• Lee, Kichun

• Wavelets
• Classification
• Feature extraction

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/1853/61244

OAI identifier oai:identifier

oai:repository.gatech.edu:1853/61244