Design of bivariate sinc wavelets

This paper introduces a new way of constructing 2-D wavelets which generalizes the univariate sinc wavelets to images sampled on arbitrary lattices. For lattices other than Cartesian, such wavelets are no longer tensor products of the univariate version. The proposed construction method is based on the zonotope decomposition of the Brillouin zone of the lattice and can be generalized to all 2-D or 3-D lattices. While our construction allows for the derivation of sinc wavelets for any 2-D lattice, we particularly study the case for the hexagonal lattice. We present experiments that contrast Cartesian tensor-product wavelet decomposition against the non-separable hexagonal wavelet decomposition and demonstrate the increased isotropy in the latter case.