An entropy-based signal restoration method on graphs

This paper proposes an entropy-based best tree decomposition and reconstruction method for signals on graphs. A recently popular method for graph signal decomposition is to down-sample and filter a graph signal by low-pass and high-pass filters, then iterate decomposition on every low-pass component. This method is not well-suited for graph signals with significant high frequency components. We propose a new method to decompose a graph signal according to an entropy based best tree decomposition scheme. This method is adaptive for graph signal decomposition, and it gives more accurate and robust representations for graph signals. The proposed decomposition method is shown to provide an efficient representation well-suited for graph signal compression, or graph-based image compression. The performance of the proposed method is validated by real-world graph signal recovery problems. The new method also achieves better performance than the existing wavelet-like decomposition in graph-based image decomposition and reconstruction. Keywords— Graph Fourier transform, graph signal filter, entropy, graph signal compression.