Graph Signal Processing

Graph Signal Processing treats measurements attached to connected entities—such as sensors, brain regions, or traffic locations—as signals whose structure follows a graph, enabling analysis beyond regular grids. Common tools include graph Laplacians and graph Fourier transforms, spectral and polynomial filters, wavelets, sampling and compressed sensing, and learned graph structures. Current work extends these tools to time-varying and directed graphs, hypergraphs, and sheaves, with applications including denoising, interpolation, anomaly detection, recommendation, and generative modeling. A central tension is that smoothness makes signals easier to estimate and compress but can erase high-frequency or heterophilous structure; methods must also balance robustness to graph errors with fidelity and scalability.