Abstract
Signal processing on graphs extends signal processing concepts and methodologies from the classical signal processing theory to data indexed by general graphs. For a bandlimited graph signal, the unknown data associated with unsampled vertices can be reconstructed from the sampled data by exploiting the spatial relationship of graph signal. In this paper, we propose a generalized analytical framework of unsampled graph signal and introduce a concept of diffusion operator which consists of local-mean and global-bias diffusion operator. Then, a diffusion operator-based iterative algorithm is proposed to reconstruct bandlimited graph signal from sampled data. In each iteration, the reconstructed residuals associated with the sampled vertices are diffused to all the unsampled vertices for accelerating the convergence. We then prove that the proposed reconstruction strategy converges to the original graph signal. The simulation results demonstrate the effectiveness of the proposed reconstruction strategy with various downsampling patterns, fluctuation of graph cut-off frequency, robustness on the classic graph structures, and noisy scenarios.
Highlights
Recent years have witnessed an enormous growth of interest in efficient paradigms and techniques for representation, analysis, and processing of large-scale datasets emerging in various fields and applications, such as sensor and transportation networks, social networks and economic networks, and energy networks [1, 2]
The main contribution of this paper is that we present a generalized analytical framework of graph signals associated with the unsampled vertices to further improve the convergence rate of bandlimited graph signal reconstruction
We proposed a localmean diffusion operator, which is used to assign the reconstructed residual from the sampled vertices to their adjacent unsampled vertices, to achieve the local-mean diffusion operation
Summary
Recent years have witnessed an enormous growth of interest in efficient paradigms and techniques for representation, analysis, and processing of large-scale datasets emerging in various fields and applications, such as sensor and transportation networks, social networks and economic networks, and energy networks [1, 2]. The irregular structure is the most important characteristic of those large-scale datasets, which limits the applicability of many approaches used for small-scale datasets. This big data problem motivates the emerging field of signal processing on graphs. Graphs are useful representation tools for representing large-scale datasets with geometric structures. The relational structure of large-scale dataset is represented with graph, in which data elements correspond to the vertices, the relationship between data elements
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