Omnibus Change Detection in Block Diagonal Covariance Matrix PolSAR Data Illustrated With Simulated and Sentinel-1 Data

Abstract

This article describes the latest developments in our work on complex Wishart distribution-based detection of change in time series of multilook polarimetric synthetic aperture radar data in the covariance matrix representation. These developments include better approximations of the probability measures associated with the omnibus test statistics $\bm {Q}$ and $\bm {R}_{\bm {j}}$ for block diagonal data in general, including the important cases with diagonal only Sentinel-1 data as obtained from Google Earth Engine and reflection symmetry data for full polarimetry. Additionally, the article introduces an omnibus version of the Loewner (or Löwner) order with visualization of change over time, where the omnibus change path shows significant difference. We also find the time point with the greatest change along the omnibus change path. The processing is illustrated with generated data and a series of 15 Sentinel-1A scenes covering Frankfurt Airport, Germany. Results show that the new and better approximations of the probability measures for the test statistics are important for the assignment of labels “change” or “no change” to a pixel or a patch, especially in “no change” regions. Furthermore, compared to the use of the full covariance matrix, the probability measures associated with the diagonal only test statistics incorrectly detect more change in these “no change” regions for the Sentinel-1 diagonal only data. Hence, the use of the full 2 $\bm {\times }$ 2 covariance matrix if avalable is important. Finally, the omnibus Loewner order gives far fewer false detections than its pairwise counterpart.

Keywords

• Greatest change
• omnibus likelihood ratio test statistic
• omnibus Loewner order
• polarimetric synthetic aperture radar (PolSAR)