Automation of the lifting factorisation of wavelet transforms
The lifting scheme for finding the discrete wavelet transform depends on the factorization of polyphase matrices, whose entries are Laurent polynomials. Such factorization is not unique. In this paper, the authors outline a Mathematica program that finds all factorizations of such matrices by automating the Euclidean algorithm for Laurent polynomials. Gröbner bases are used to the reduce polynomial degree and the number of wavelet coefficients.
scientific article; zbMATH DE number 1485018