In this paper we propose a new wavelet transform applicable to functions
defined on graphs, high dimensional data and networks. The proposed method
generalizes the Haar-like transform proposed in \cite{gavish2010mwot}, and it
is similarly defined via a hierarchical tree, which is assumed to capture the
geometry and structure of the input data. It is applied to the data using a
multiscale filtering and decimation scheme, which can employ different wavelet
filters. We propose a tree construction method which results in efficient
representation of the input function in the transform domain. We show that the
proposed transform is more efficient than both the 1D and 2D separable wavelet
transforms in representing images. We also explore the application of the
proposed transform to image denoising, and show that combined with a subimage
averaging scheme, it achieves denoising results which are similar to the ones
obtained with the K-SVD algorithm.