Irregularity-Aware Bandlimited Approximation for Graph Signal Interpolation

Abstract: In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions, leading to suboptimal performance. In the context of sampling and reconstruction, graph irregularities lead to varying contributions from sampled nodes for interpolation and differing levels of reliability for interpolated nodes. The existing GFT-based methods in the literature make bandlimited signal approximations without considering graph irregularities and the relative significance of nodes, resulting in suboptimal reconstruction performance under various mismatch conditions. In this paper, we leverage the GFT equipped with a specific inner product to address graph irregularities and account for the relative importance of nodes during the bandlimited signal approximation and interpolation process. Empirical evidence demonstrates that the proposed method outperforms other GFT-based approaches for bandlimited signal interpolation in challenging scenarios, such as sampling sets selected independently of the underlying graph, low sampling rates, and high noise levels.