Microlocal filtering with multiwavelets

Abstract

AbstractHyperfunctions in Rn are intuitively considered as sums of boundary values of holomorphic functions defined in infinitesimal wedges in Cn. Orthonormal multiwavelets, which are a generalization of orthonormal single wavelets, generate a multiresolution analysis by means of several scaling functions. Microlocal analysis is briefly reviewed and a multiwavelet system adapted to microlocal filtering is proposed. A rough estimate of the microlocal content of functions or signals is obtained from their multiwavelet expansions. A fast algorithm for multiwavelet microlocal filtering is presented and several numerical examples are considered