Author: Ma, Chun-yat
Title: Adaptive wavelet and multiwavelet denoising
Degree: M.Phil.
Year: 2008
Subject: Hong Kong Polytechnic University -- Dissertations.
Wavelets (Mathematics)
Signal processing -- Digital techniques.
Department: Department of Electronic and Information Engineering
Pages: xx, 124 p. : ill. ; 30 cm.
Language: English
Abstract: The wavelet and multiwavelet transforms have been successfully used in many signal denoising applications due to their localization and multiresolution properties. In this work, adaptive denoising schemes in wavelet and multiwavelet domain are studied. As the first part of this work, the problem of speech enhancement using the multitaper spectrum (MTS) estimation technique is investigated. We show that the variance of noise in the log MTS domain varies significantly according to the magnitude of the underlying speech MTS. Thus a spectrally adaptive wavelet denoising scheme, which allows the threshold to be adjusted according to the underlying speech MTS, is suggested to assist in estimating the power spectrum of the original speech signal. Simulation results show that the proposed algorithm consistently outperforms the traditional speech enhancement methods evaluated using both subjective and objective measures. It leads to speeches with better intelligibility without increasing the background noise. The second part of this work concerns the denoising of sparse signals. For such kind of signals, traditional wavelet denoising schemes may fail due to insufficient signal wavelet coefficients to reliably determine the required statistics. However, the traditional approaches can be enhanced by an adaptive denoising scheme based on the cross correlation between the vector elements of multiscaling coefficients. Our investigation shows that the behavior of the cross correlation between the vector elements of the multiscaling coefficients for signal and noise is different. Based on this dissimilarity, we can effectively identify the regions of the signal where noise coefficients are dominated. Such coefficients are then removed accordingly. Besides, the traditional multivariate shrinkage can also be applied to the remaining multiwavelet coefficients to further reduce the noise energy. Nevertheless, in order to practically apply the algorithm, there is a need to derive efficient realization methods for the discrete multiwavelet transform. In this thesis, we propose a generalized algorithm for the realization of multifilters. The algorithm is based on an improved order-one factorization method that efficientiy decomposes the polyphase matrix of multifilters into a chain of order-one matrices. Each matrix is further simplified by applying a special form of Givens rotation. The new approach greatly reduces the computational complexity of realizing the discrete multiwavelet transform. On the whole, we show in this thesis that adaptive wavelet and multiwavelet denoising schemes can significantly outperform the traditional methods particularly for signals with varying statistical characteristics. They will play a more important role in the future signal processing researches as it does not only enhance signals in a statistical sense, but can be easily perceived by the users.
Rights: All rights reserved
Access: open access

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