  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. We modify the filter-bank decomposition scheme of the redundant wavelet
transform by adding in each decomposition level linear 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 to image denoising,
and show that it achieves denoising results that are close to those obtained
with the BM3D algorithm.
