Lifting Based Wavelet Transforms on Graphs

We present a novel method to implement lifting based wavelet transforms on general graphs. The detail and approximation coefficients computed from this graph transform can be interpreted similarly to their counterparts in standard signal processing process. Our approach is based on partitioning all nodes in the graph into two sets, containing "even" and "odd" nodes, respectively. Then, as in standard lifting, nodes of one parity are used to predict/update those of the other. We discuss the even-odd assignment problem on the graph and provide a solution that is well suited to construct the transform. As an example we discuss how our transform could be used in a denoising application. I. I NTRODUCTION

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