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Perfect Reconstruction Filter Banks for the Hexagon Grid

We introduce two new perfect reconstruction (P.R.) decompositions for signals on a hexagon lattice. One is an orthogonal compaction (coding) transform similar to that used in the Simoncelli-Adelson quadtree pyramid, but with perfect reconstruction and compact integer-valued filters. The other is a 3-ary "blurring" filter bank which has a perfect inverse ("sharpening") filter bank. Each example filter bank has better properties than other banks proposed for the hexagon grid, and, it would seem, better properties than any possible comparable filter bank for the square grid