Research On The Orthonormal Bases Of Compactly Supported Wavelets And Application To Digital Watermark

This dissertation mainly contains two contents: constructions of Daubechies wavelet, Coiflet and Coifrnan packet; and studies of digital watermarking algorithms in domains of wavelet and wavelet packet.Wavelet analysis has been developed rapidly in both theory and application during the last twenty years since the wavelet concept was introduced in 1984 by J.Morlet and A.Grossmann. The main advantages of wavelet are the time-frequency localization and multiresolutional properties. Theory and practice have proven that wavelet transform is an effective method for signal-image processings.With development of internet, the copyright protection has become a matter of great urgency. As an effective technique for copyright protection of digital products, the digital watermark has been developed rapidly in the past a few years. It becomes necessary to combine digital watermark with wavelet transform because of the wavelet favorable characteristics. Theory and experiment have proven that digital watermarking algorithms based on wavelet and wavelet packet domains have good robustness and imperceptibility.The Daubechies wavelet is an effective and popular basis in signal and image processings. This wavelet has maximum vanishing moment for a given support width. Daubechies gave two types of orthonormal bases of compactly supported wavelets: with the extremely phase for N=2,3,...10(nine wavelets) and with the least asymmetry for N=4,5,...10(seven wavelets).According to Bezout's theorem, the Daubechies wavelets are a finite set for a given order N of vanishing moment. Available Daubechies wavelets are only part of the solution set. We have derived all solutions of Daubechies wavelet for each order N from 2 to 10 using homotopy method. The relevant properties are givenas follows: scaling filter H(ω) and coefficients {h_k},plots of scaling and waveletφ(t),φ|^(ω),Ψ(t).The Coifman wavelet (Coiflet) has better symmetry and better regularity than the...