Redundant Wavelets on Graphs and High Dimensional Data Clouds

In this paper, we propose a new redundant wavelet transform applicable to scalar functions defined on high dimensional coordinates, weighted graphs and networks. The proposed transform utilizes the distances between the given data points to construct tree-like structures. We modify the filter-bank decomposition scheme of the redundant wavelet transform by adding in each decomposition level operators that reorder the approximation coefficients. These reordering operators are derived by organizing the tree-node features so as to shorten the path that passes through these points. We explore the use of the proposed transform for the recovery of labels defined on point clouds and to image denoising, and show that in both cases the results are promising.