In this paper, a simple method is proposed for the design of biorthogonal wavelet bases. Starting from any simple orthogonal wavelets, we showed bow using the wavelet lifting scheme, a new completely arbitrary biorthogonal wavelets can be constructed to suit any specific design specifications. Two specific applications are considered. The first application is to design biorthogonal filter banks with perfect reconstruction property, whereas the second application lies in choosing the best wavelet bases for signal compression applications. In the first application, it is shown that unlike traditional orthogonal QMF banks, where the analysis and synthesis filters are closely related, biorthogonal filter banks have the feature that the analysis and synthesis filters can be freely chosen to meet any design specifications, while maintains perfect construction property PR. The flexibility in designing these filter banks is achieved by optimizing the parameters of the lifting some used in their construction. In the de-noising application, the strategy is to use the lifting scheme to get the optimum wavelet bases that will lead to the minimum energy norm L{sub}2 up to scale L. Illustrative examples are given to demonstrate the simplicity and efficiency of the proposed design approach.
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