High-order balanced M-band orthogonal multiwavelet: Construction and application

Abstract

This article proposed an approach to construct high-order balanced M-band (M>2) orthogonal multiwavelets with symmetric property, and demonstrated the advantages of our constructed multiwavelet systems in digital elevation model (DEM) generalization application over some other wavelet systems. We studied the theories related to the key properties of M-band multiwavelets, such as orthogonality, symmetry, flipping and the particular issue and balancing. According to the theories, we then discussed the construction procedures of the M-band multiwavelet systems integrating all the key properties, and presented their realization process based on Gröbner base technique. Three families of orthogonal multiwavelets were achieved in this way, including three-band symmetric family, three-band flipped family and four-band symmetric family. Each family was indexed by a increasingly balanced order ρ (ρ∈{1,2,3}), and supported with the minimal length according to every balanced order. We finally tested their practical performance in DEM generalization application. The results show the superiority of the constructed M-band multiwavelet systems over other widely-used wavelet systems, including multiwavelet of two-band and scalar wavelets of M-band and 2-band, and justified the effectiveness of high-order balanced property of these proposed multiwavelet systems in preserving main trend features of signals.