COMPACTLY SUPPORTED BIDIMENSIONAL WAVELET BASES WITH HEXAGONAL SYMMETRY

We study a class of subband coding schemes allowing perfect reconstruction for a bidimensional signal sampled on the hexagonal grid. From these schemes we construct biorthogonal wavelet bases of L2(R2) which are compactly supported and such that the sets of generating functions psi1, psi2, psi3 for the synthesis and psi1, psi2, psi3 for the analysis, as well as the scaling functions phi and phi, are globally invariant by a rotation of 2pi/3. We focus on the particular case of linear splines and we discuss how to obtain a higher regularity. We finally present the possibilities of sharp angular frequency resolution provided by these new bases.