We present two-dimensional nonseparable wavelets defined on a triangular lattice using an average interpolating lifting scheme. With the update-first form of the lifting scheme, a primal scaling function and three dual wavelets are found to be based on the Haar functions defined on the lattice. However, the construction of a dual scaling function and three primal wavelets with arbitrary order is possible, and all analysis filters intrinsically have two-dimensional support. These filters are applied to the image compression task, and we show that filters constructed with the update-first form of the lifting scheme outperform the original filters constructed with a standard predict-update form of the lifting scheme.
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