Sampling Signals on Graphs: From Theory to Applications
arXiv:2003.03957 · doi:10.1109/MSP.2020.3016908
Abstract
The study of sampling signals on graphs, with the goal of building an analog of sampling for standard signals in the time and spatial domains, has attracted considerable attention recently. Beyond adding to the growing theory on graph signal processing (GSP), sampling on graphs has various promising applications. In this article, we review current progress on sampling over graphs focusing on theory and potential applications. Although most methodologies used in graph signal sampling are designed to parallel those used in sampling for standard signals, sampling theory for graph signals significantly differs from the theory of Shannon--Nyquist and shift-invariant sampling. This is due in part to the fact that the definitions of several important properties, such as shift invariance and bandlimitedness, are different in GSP systems. Throughout this review, we discuss similarities and differences between standard and graph signal sampling and highlight open problems and challenges.
References in corpus (28)
- The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
- Discrete Signal Processing on Graphs
- Discrete Signal Processing on Graphs: Sampling Theory
- Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies
- Signals on Graphs: Uncertainty Principle and Sampling
- Sampling of graph signals with successive local aggregations
- Near-Optimal Sensor Placement for Linear Inverse Problems
- Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs
- Fast Resampling of 3D Point Clouds via Graphs
- Matrix Completion on Graphs
- Greedy Sampling of Graph Signals
- Eigendecomposition-Free Sampling Set Selection for Graph Signals
- Sensor placement by maximal projection on minimum eigenspace for linear inverse problems
- Irregularity-Aware Graph Fourier Transforms
- Spectral Domain Sampling of Graph Signals
- Approximate fast graph Fourier transforms via multi-layer sparse approximations
- Spectral Projector-Based Graph Fourier Transforms
- Two-Channel Critically-Sampled Graph Filter Banks With Spectral Domain Sampling
- Fast Graph Sampling Set Selection Using Gershgorin Disc Alignment
- Generalized Sampling on Graphs With Subspace and Smoothness Priors
- Low-complexity Graph Sampling with Noise and Signal Reconstruction via Neumann Series
- Sparse Sampling for Inverse Problems with Tensors
- Fast Graph Fourier Transforms Based on Graph Symmetry and Bipartition
- Graph Sampling for Matrix Completion Using Recurrent Gershgorin Disc Shift
- Localized Iterative Methods for Interpolation in Graph Structured Data
- Diverse Landmark Sampling from Determinantal Point Processes for Scalable Manifold Learning
- On the Supermodularity of Active Graph-based Semi-supervised Learning with Stieltjes Matrix Regularization
- What's in a frequency: new tools for graph Fourier Transform visualization
Cited by in corpus (16)
- Graph Signal Processing: History, Development, Impact, and Outlook
- 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
- Graph-signal Reconstruction and Blind Deconvolution for Structured Inputs
- Two Channel Filter Banks on Arbitrary Graphs with Positive Semi Definite Variation Operators
- Widely-Linear MMSE Estimation of Complex-Valued Graph Signals
- Reconstructing nodal pressures in water distribution systems with graph neural networks
- Spectral Domain Spline Graph Filter Bank
- Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation
- Graph Blind Deconvolution with Sparseness Constraint
- A Bayesian Perspective on Uncertainty Quantification for Estimated Graph Signals
- Learning Graph Filters for Structure-Function Coupling based Hub Node Identification
- Maximal Independent Sets for Pooling in Graph Neural Networks
- A low discrepancy sequence on graphs