LaWeCo: Active region detection in non-uniformly sampled data using Laplacian-weighted covariance
Event detection in sparse, non-uniformly sampled multidimensional data eludes traditional signal processing techniques. We propose a method that, within the graph-theoretic framework, successfully addresses the task of localizing and characterizing active regions by leveraging the coherent behavior detection capabilities of the covariance matrix together with the natural definition of graph neighborhood connectivity provided by the Laplacian. We further extend this framework using scale space formulation to detect the extent of active region. Our method exhibits significant improvement in detecting active regions compared to other similar state-of-the art techniques. The method is demonstrated on interferometric synthetic aperture radar (InSAR) data that is both sparse and non-uniformly sampled. Comparison with three widely used event detection methods reveals the efficacy and efficiency of the Laplacian-weighted covariance technique.