Generalized Tree-Based Wavelet Transform

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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...
Idan Ram, Michael Elad, Israel Cohen
Added 22 Mar 2011
Updated 22 Mar 2011
Type Journal
Year 2010
Where CORR
Authors Idan Ram, Michael Elad, Israel Cohen
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