Generalized Sampling on Graphs With Subspace and Smoothness Priors
arXiv:1905.04441 · doi:10.1109/TSP.2020.2982325
Abstract
We propose a framework for generalized sampling of graph signals that parallels sampling in shift-invariant (SI) subspaces. This framework allows for arbitrary input signals, which are not constrained to be bandlimited. Furthermore, the sampling and reconstruction filters may be different. We present design methods of the correction filter that compensate for these differences and lead to closed form expressions in the graph frequency domain. In this study, we consider two priors on graph signals: The first is a subspace prior, where the signal is assumed to lie in a periodic graph spectrum (PGS) subspace. The PGS subspace is proposed as a counterpart of the SI subspace used in standard sampling theory. The second is a smoothness prior that imposes a smoothness requirement on the graph signal. We suggest the use of recovery techniques for when the recovery filter can be optimized and under a setting in which a predefined filter must be used. Sampling is performed in the graph frequency domain, which is a counterpart of "sampling by modulation" used in SI subspaces. We compare our approach with existing sampling techniques on graph signal processing. The effectiveness of the proposed generalized sampling approach is validated numerically through several experiments.
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Cited by in corpus (11)
- Sampling Signals on Graphs: From Theory to Applications
- Bayesian Estimation of Graph Signals
- Graph Signal Sampling Under Stochastic Priors
- Graph Signal Processing: Dualizing GSP Sampling in the Vertex and Spectral Domains
- Graph Signal Restoration Using Nested Deep Algorithm Unrolling
- Localized Fourier Analysis for Graph Signal Processing
- Graph Signal Processing -- Part III: Machine Learning on Graphs, from Graph Topology to Applications
- Task-Based Graph Signal Compression
- Sampling and Recovery of Graph Signals based on Graph Neural Networks
- A Bayesian Perspective on Uncertainty Quantification for Estimated Graph Signals
- Graph Blind Deconvolution with Sparseness Constraint