Passive and Active Sampling for Piecewise-Smooth Graph Signals

In this work, we study the sampling of piecewise smooth- graph signals that exhibit an inhomogeneous level of smoothness over the graph and are characterized by have abrupt, localized discontinuities between smooth regions of the graph. We propose an extension to the graph trend filtering framework under the sampling setting and present an ADMM-algorithm to efficiently reconstruct piecewise-smooth graph signals. Further, to alleviate the limitations of passive sampling in this setting, we develop an active sampling strategy that incorporates feedback to focus the sampling procedure near the boundary or discontinuities. We then conduct experiments that exhibit the performance of our algorithm on large complex graphs and validate the efficacy of our sampling strategies.