New Robust Statistics for Change Detection in Time Series of Multivariate SAR Images

Abstract

This paper explores the problem of change detection in time series of heterogeneous multivariate synthetic aperture radar images. Classical change detection schemes have modelled the data as a realisation of Gaussian random vectors and have derived statistical tests under this assumption. However, when considering high-resolution images, the heterogeneous behaviour of the scatterers is not well described by a Gaussian model. In this paper, the data model is extended to Spherically Invariant Random Vectors where the heterogeneity of the images is accounted for through a deterministic texture parameter. Then three separate detection problems are considered and generalised likelihood ratio test technique is used to derive statistical tests for each problem. The constant false alarm rate property of the new statistics are studied both theoretically and through simulation. Finally, the performance of the new statistics are studied both in simulation and on real synthetic aperture radar data and compared to Gaussian-derived ones. The study yields promising results when the data are heterogeneous.

Robust Low-Rank Change Detection for Multivariate SAR Image Time Series

“…The rationale behind this is that a local change is translated by a change in the second-order statistics of the observations. To perform this test, the GLRT approach has been successfully applied in numerous works [6]- [13], [25], [28]. The following subsections recall existing GLRTs (depending on the assumed model) that have been applied to CD in SAR-ITS.…”

“…This issue can be alleviated by assuming a compound Gaussian model, as described in section II-C. Under this assumption, the CD can be performed by testing a change in both the covariance matrix and the texture parameters [25]. The corresponding GLRT, denotedΛ CG , corresponds to (1) and (3) with the following distribution/parameters:…”

“…The evaluation of the quantityΛ CG involves fixed-point equations that can be computed numerically. A study and generalizations (testing for textures or covariance matrices individually) of this approach can be found in [25].…”

“…In this case, Compound Gaussian models have been shown to provide a better fit to empirical measurements [20], [21], which is interesting to leverage in SAR images processing (e.g., in [22] for classification). In order to account for signals non-Gaussianity in SAR-ITS, [23]- [25] proposed various Generalized Likelihood Ratio Tests (GLRTs) assuming a Compound Gaussian distribution. Specifically, [25] extended the Gaussian GLRT for covariance equality testing to the case of Compound Gaussian models, which was shown to yield improvements in terms of CD performance.…”

“…In order to account for signals non-Gaussianity in SAR-ITS, [23]- [25] proposed various Generalized Likelihood Ratio Tests (GLRTs) assuming a Compound Gaussian distribution. Specifically, [25] extended the Gaussian GLRT for covariance equality testing to the case of Compound Gaussian models, which was shown to yield improvements in terms of CD performance. ii) Second, the standard detectors are derived assuming unstructured covariance matrices, while the signal of interest usually lies in a low-dimensional subspace.…”