A design of triangular biorthogonal wavelet filters with average interpolation scheme

We propose a method to construct a new family of triangular biorthogonal wavelet filters based on the Donoho's average interpolating wavelets fitted into the lifting scheme. Using the update-first form of two-dimensional lifting on an equilateral triangular lattice, we show that all of analysis filters have truly two-dimensional distribution. While a primal LP filter turns out to be based on the Haar filter, the construction of three primal HP filters with an arbitrary order is possible.