  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.
