Bandlimited graph signal reconstruction by diffusion operator

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.

Erratum to: Bandlimited graph signal reconstruction by diffusion operator

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Following publication of this article [1], it has come to our attention that the acknowledgements were captured incorrectly and the correct acknowledgements should include the following:

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Local Measurement and Diffusion Reconstruction for Signals on a Weighted Graph

“…Note that the unsampled vertices of a graph signal are influenced by all the sampled vertices, which should not be limited in the local sets. Based on a local-mean diffusion operator and a global-bias diffusion operator, Yang et al [10] proposed the iterative global diffusion reconstruction (IGDR), which improved the IPR. In some potential applications, the obtained data may be a combination of signals associated with several vertices, Wang proposed the iterative local measurement reconstruction (ILMR) to reconstruct the bandlimited graph signals [11].…”