Nonlinear multi-scale statistical identification approach for data processing enhancing and quantitative study

Abstract

Integration of the nonlinear approaches for system identification is proposed for spectral differentiation and object recognition in this research. Multi-scale nonlinear principal component analysis (NCA) has been implemented to analyze the individual components of approximations and details based on wavelet transform. Neural network training has been applied to NCA while both 1D and 2D wavelet transform have been conducted across different scales. At each scale, the principal components are selected in order to reconstruct the intrinsic signal and image. This statistical identification approach is essential to enhance multivariate data processing. Case studies on signal and image processing are both conducted. In addition, quantitative measures are presented to analyze the nonlinear multi-scale approach from the objective perspectives.