An algorithm for constructing the two-direction Armlet multiwavelet

Abstract

In this paper, an algorithm is discussed for constructing the two-direction Armlet multiwavelet. First, the definition of two-direction Armlet multiwavelet is presented in this paper. A two-direction multiwavelet can be changed to a special multi-wavelet. By Two-scale Similar Transform (TST), a transform can be taken on the two-scale matrix symbols of a two-direction multi-wavelets. This transform keeps the orthogonality of the two-direction multi-wavelets. However, the condition is discussed which the two-direction multi-wavelet corresponding to a two-direction multi-scaling function is an Armlet with order n. An approach is given for constructing the transform matrix. Finally, an example is given for discussing the two-direction Armlet multi-wavelet with order 2.