A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D
Brigitte Forster, EPFL LIB

Test Run • 11 July 2003

Abstract
We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis elements have nice properties in Hilbert space such as smoothness of fractional order (alpha in R+) and fast decay. The corresponding filters allow a FFT-based implementation and thus provide a fast algorithm for the wavelet transform.