Generalized Tree-Based Wavelet Transform

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 [1], and it is 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 modified version of the common 1D wavelet filtering and decimation scheme, which can employ different wavelet filters. In each level of this wavelet decomposition scheme, a permutation derived from the tree is applied to the approximation coefficients, before they are filtered. We propose a tree construction method that results in an efficient representation of the input function in the transform domain. We show that the proposed transform is more efficient than both the one-dimensional (1D) and two-dimensional (2D) separable wavelet transforms in representing images. We also explore the application of the proposed transform to image denois...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Idan Ram, Michael Elad, Israel Cohen
• Keywords: CORR 2010, Education, Subimage Averaging Scheme, Wavelet, Wavelet Decomposition Scheme