Construction of Biorthonormal Multiresolution Analysis with Length 4
Jiu Liu, Pla Information · Chinese Journal of Computers · 2002
By Lawton's condition, it is known that whether two banks of filter coefficients can generate a pair of biorthonormal MRAs depends upon whether the eigenvalues of the so called transition operators defined by these filter coefficients are less than 1. Since such transition operators can be expressed equivalently by matrices, by computing The eigenvalues of the matrices, this paper discusses the conditions the filter coefficients satisfy such that they can generate a pair of biorthonormal MRAs. Therefore, the domains of the filter real coefficients which can generate biorthonormal MRAs and orthonormal MRAs are obtained. Finally, some examples of wavelet are given, and their validity applied to image compression is analyzed by calculating their entropy and peak signal-to-noise ratio. The results show that some wavelets are better than the famous Daubechies wavelet with filter length 4.