Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation.
This paper addresses the problem of selecting an optimal sampling set for signals on graphs. The proposed sampling set selection (SSS) is based on a localization operator that can consider both vertex domain and spectral domain localization. We clarify the relationships among the proposed method, sensor position selection methods in machine learning, and conventional SSS methods based on graph frequency. In contrast to the conventional graph signal processing-based approaches, the proposed method does not need to compute the eigendecomposition of a variation operator, while still considering (graph) frequency information. We evaluate the performance of our approach through comparisons of prediction errors and execution time.
We describe a method of oversampling signals defined on a weighted graph by using an oversampled graph Laplacian matrix. The conventional method of using critically sampled graph filter banks has to decompose the original graph into bipartite subgraphs, and a transform has to be performed on each subgraph because of the spectral folding phenomenon caused by downsampling of graph signals. Therefore, the conventional method cannot always utilize all edges of the original graph in a single stage transformation. Our method is based on oversampling of the underlying graph itself, and it can append nodes and edges to the graph somewhat arbitrarily. We use this approach to make one oversampled bipartite graph that includes all edges of the original non-bipartite graph. We apply the oversampled graph with the critically sampled graph filter bank or the oversampled one for decomposing graph signals and show the performances on some experiments.
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