A Nonparametric Estimator for Coherent Change Detection: The Permutational Change Detection

Nowadays, synthetic aperture radar (SAR) is widely used in heterogeneous fields with aims strictly dependent on the objectives of the application. One of the most common is the exploitation of the interferometric-SAR (InSAR) to measure millimeter movements on the Earth's surface, aiming to monitor failures (e.g., landslides) or to measure the health state of infrastructures (e.g., mining assets, bridges, and buildings). In this article, developing algorithms to detect temporal and spatial changes in the radar targets becomes very important. This article focuses on the temporal change detection framework, proposing a nonparametric coherent change detection (CCD) algorithm called permutational change detection (PCD), a purely statistical algorithm whose core is the permutational test. The PCD estimates the temporal change points (CPs) of a radar target recognizing blocks structure in the coherence matrix, namely, new radar objects. The algorithm has been fine-tuned for small SAR datasets, with the specific aim of prioritizing the analysis of the latest changes. A rigorous mathematical derivation of the algorithm is carried out, explaining how some limits have been addressed. Then, the performance analysis on the simulated data is deeply accomplished, carried out for the stand-alone PCD and the PCD compared with a parametric CCD algorithm based on the generalized likelihood ratio test (GLRT), and with the Omnibus and REACTIV detectors. The comparison with these other algorithms and the stand-alone performance analysis point out the robustness of the PCD in dealing with very noisy environments, even in the case of a single block. Finally, the PCD is validated by processing two Sentinel I data stacks, ascending and descending geometries, of the 2016 Central Italy earthquake.