Construction of triangular biorthogonal wavelet filters for isotropic image processing

We propose new non-separable two dimensional biorthogonal wavelets whose filters are defined on the regular triangular lattice on a plane. Their construction uses lifting in the polyphase representation of the filters. While filters of arbitrary orders may be obtained by following the same way as in 1D case, in this paper we focus our attention mainly on the construction method using a few simple examples. Applying one of the example filters to simple images, we show that isotropy of images are improved in the wavelet transform as compared with the usual tensor product wavelet transform.