Discrete Wavelet Denoising via Kernel Based Nonlinear Component Analysis: Case Studies

All 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 the subsequent levels, while the 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.