Author:

Keywords:

Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, COMPACTLY SUPPORTED WAVELETS, QUADRATURE MIRROR FILTERS, PERFECT-RECONSTRUCTION, ORTHONORMAL BASES, BANKS, FIR, DISCRETE, SPACES, MULTIRESOLUTION, DECOMPOSITIONS, 0101 Pure Mathematics, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, Numerical & Computational Mathematics, 4901 Applied mathematics, 4904 Pure mathematics

Abstract:

We present the lifting scheme, a new idea for constructing compactly supported wavelets with compactly supported duals. The lifting scheme uses a simple relationship between all multiresolution analyses with the same scaling function. It isolates the degrees of freedom remaining after fixing the biorthogonality relations. Then one has full control over these degrees of freedom to custom design the wavelet for a particular application. The lifting scheme can also speed up the fast wavelet transform. We illustrate the use of the lifting scheme in the construction of wavelets with interpolating scaling functions. © 1996 Academic Press, Inc.