On Bandwidth and Scale Selection in Processing of Time-Varying Signals with Applications

This dissertation, "On Bandwidth and Scale Selection in Processing of Time-varying Signals With Applications" by Zhiguo, Zhang, 張治國, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the Dissertation Entitled On Bandwidth and Scale Selection in Processing of Time-varying Signals with Applications submitted by ZHANG Zhiguo for the degree of Doctor of Philosophy at the University of Hong Kong in October 2007 This dissertation studies adaptive local bandwidth and scale selection methods in processing of time-varying signals and their applications. Generally, the time-varying signals are modeled locally using a window with a certain bandwidth. Since signals may vary considerably over time, it is crucial to adaptively select a proper local bandwidth so as to achieve a better bias-variance tradeoff in estimating the local model parameters. The dissertation aims to develop the adaptive bandwidth selection methods and applications on three issues: local polynomial regression (LPR), time-frequency analysis (TFA), and Kalman filter. First, in the LPR model, the observations are modeled locally by a polynomial using least-squares (LS) criterion with a kernel having a certain bandwidth. A new refined intersection confidence intervals (RICI) method is proposed to adaptively determine the optimal local bandwidth. Furthermore, motivated by the sensitivity of LS-based LPR in impulsive noise environment, M-estimation is introduced to suppress the outliers. The resultant M-estimation-based LPR with RICI method (M-LPR-RICI) can be widely applied in curve estimation, multi-resolution analysis and image processing. Moreover, in its application to image processing, LPR employs a steering kernel with local orientation instead of the conventional symmetric kernel to adapt better to local image characteristics. Experimental results show that the proposed M-LPR-RICI method delivers a considerably better performance than conventional LPR-based methods. Secondly, in TFA techniques, the bias-variance tradeoff problem exhibits as the tradeoff between time resolution and frequency resolution, and is concerned with the choice of window length in the TFA methods. The RICI method is applied to two TFA methods based on Lomb periodogram and minimum variance spectral estimation (MVSE) to adaptively select window lengths in the time-frequency domain. Simulation results show that the two TFA methods with adaptive window selection can obtain good time-frequency resolution in estimating various frequency components. In addition, according to the time-frequency characteristics of click-evoked otoacoustic emissions (CEOAEs), a frequency-dependent windowed MVSE is proposed to achieve better frequency resolution in TFA of CEOAEs than the wavelet transform. Finally, we consider the adaptive bandwidth selection in the Kalman filter algorithm. By modeling a time-varying signal as an autoregressive (AR) process and setting a smoothness constraint on the AR coefficients, a new Kalman filter with variable number of measurements method (KFVNM) can be used to estimate the AR coefficients. The number of measurements used in the KFVNM method is adaptively selected to achieve a better bias-variance tradeoff for the system state estimate than the conventional Kalman filter. The KFVNM method is applied to power spectral density (PSD) estimation of cardiovascular pressure signals and subspace-based direction of arrivals (DOA) tracking. The good performances demonstrate the advantages of the proposed KFVNM algorithm. In conclusion, adaptive bandwidth selection meth