Graph-wavelet filterbanks for edge-aware image processing

In our recent work, we proposed the construction of critically-sampled wavelet filterbanks for analyzing functions defined on the vertices of arbitrary undirected graphs. These graph based functions, referred to as graph-signals, provide a flexible model for representing many datasets with arbitrary location and connectivity. An application area considered in that work is image-processing, where pixels can be connected with their neighbors to form undirected graphs. In this paper, we propose various graph-formulations of images, which capture both directionality and intrinsic edge-information. The proposed graph-wavelet filterbanks provide a sparse, edge-aware representation of image-signals. Our preliminary results in non-linear approximation and denoising using graphs show promising gains over standard separable wavelet filterbank designs.