Open AccessCase Studies on Discrete Wavelet Denoising via Kernel Based Nonlinear Component Analysis
Author(s) -
Zhengmao Ye,
Hongcheng Yin,
Yongmao Ye
Publication year - 2021
Publication title -
wseas transactions on computer research
Language(s) - English
Resource type - Journals
eISSN - 2415-1521
pISSN - 1991-8755
DOI - 10.37394/232018.2021.9.2
Subject(s) - wavelet , discrete wavelet transform , noise reduction , nonlinear system , wavelet packet decomposition , frequency domain , kernel (algebra) , algorithm , mathematics , second generation wavelet transform , wavelet transform , pattern recognition (psychology) , computer science , artificial intelligence , mathematical analysis , physics , quantum mechanics , combinatorics
Complex real world problems are essentially nonlinear. Linear models are relatively simple but inaccurate to describe the nonlinear aspects of dynamic system behaviors. Denoising techniques have been broadly applied to numerous applications in the spatial domain, frequency domain, and time domain. To increase the adaptability of denoising techniques to signal processing of arbitrary nonlinear systems, kernel based nonlinear component analysis is proposed to enhance wavelet denoising. In the multilevel wavelet decomposition, the low frequency approximations and high frequency details are produced at each level. Discrete wavelet transform (DWT) will help to decompose low frequency approximations exclusively at all the succeeding levels, while wavelet packet transform decomposes both approximations and high frequency details at each level. DWT is selected for wavelet denoising in this study, where details at each level and the approximation at specified level are all subject to simplification using nonlinear component analysis. Case studies of typical nonlinear denoising problems in various domains are conducted. The results manifest strong feasibility and adaptability across diverse denoising problems of nonlinear systems.