Critically sampled graph-based wavelet transforms for image coding

In this paper, we propose a new approach for image compression using graph-based biorthogonal wavelet filterbanks (referred to as graphBior filterbanks). These filterbanks, proposed in our previous work, operate on the graph representations of images, which are formed by linking nearby pixels with each other. The connectivity and the link weights are chosen so as to reflect the geometrical structure of the image. The filtering operations on these edge-aware image graphs avoid filtering across the image discontinuities, thus resulting in a significant reduction in the amount of energy in the high frequency bands. This reduces the bit-rate requirements for the wavelet coefficients, but at the cost of sending extra edge-information bits to the decoder. We discuss efficient ways of representing and encoding this edge information. Our experimental results, based on the SPIHT codec, demonstrate that the proposed approach achieves better R-D performance than the standard CDF9/7 filter on piecewise smooth images such as depth maps.