ABSTRACT
The lifting scheme is a technique to compute classical wavelet transforms efficiently. Its time and space complexity is relatively small, when compared to the classical techniques. The lifting scheme of generating wavelets is explained via the theory of Laurent polynomials. It is used in specifying the polyphase matrix of biorthogonal wavelet with compact support. The factorization of the polyphase matrix, leads to improvement in the efficiency of the wavelet transform algorithm. This technique can also be extended to the implementation of the so-called second-generation of wavelets. The determination of greatest common divisor of two Laurent polynomials is similar to the determination of the greatest common divisor of two integers, with few differences. The biorthogonal wavelet transform is interpreted in terms of its associated polyphase matrix. A polyphase matrix is a convenient way to express the special structure of the modulation matrices. The forward and inverse biorthogonal wavelet transformations consist of several stages.
