  In our recent work, we proposed the design of perfect reconstruction
orthogonal wavelet filterbanks, called graph- QMF, for arbitrary undirected
weighted graphs. In that formulation we first designed "one-dimensional"
two-channel filterbanks on bipartite graphs, and then extended them to
"multi-dimensional" separable two-channel filterbanks for arbitrary graphs via
a bipartite subgraph decomposition. We specifically designed wavelet filters
based on the spectral decomposition of the graph, and stated necessary and
sufficient conditions for a two-channel graph filter-bank on bipartite graphs
to provide aliasing-cancellation, perfect reconstruction and orthogonal set of
basis (orthogonality). While, the exact graph-QMF designs satisfy all the above
conditions, they are not exactly k-hop localized on the graph. In this paper,
we relax the condition of orthogonality to design a biorthogonal pair of
graph-wavelets that can have compact spatial spread and still satisfy the
perfect reconstruction conditions. The design is analogous to the standard
Cohen-Daubechies-Feauveau's (CDF) construction of factorizing a maximally-flat
Daubechies half-band filter. Preliminary results demonstrate that the proposed
filterbanks can be useful for both standard signal processing applications as
well as for signals defined on arbitrary graphs.
  Note: Code examples from this paper are available at
http://biron.usc.edu/wiki/index.php/Graph Filterbanks
