Compactly supported bidimensional wavelet bases with hexagonal symmetry

AbstractWe 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 ofL2(R2) which are compactly supported and such that the sets of generating functionsψ1,ψ2,ψ3 for the synthesis and $$\tilde \psi _1 , \tilde \psi _2 , \tilde \psi _3 ,$$ for the analysis, as well as the scaling functions φ and $$\tilde \varphi $$ , are globally invariant by a rotation of 2π/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.