A joint density of interferometric and/or polarimetric images: Application to change detection

Polarimetric data of distributed scatterer can be fully characterised by the (3 × 3) Hermitian positive definite matrix which follows a complex Wishart distribution under Gaussian assumption. A second observation in time will also follow Wishart distribution. Then, these observations are correlated or uncorrelated process over time related to the monitored objects. To not to make any assumption concerning their independence, the (6 × 6) matrix which is also modelled as a complex Wishart distribution is used in this study to characterise the behaviour of the temporal polarimetric data. In particular, we derive a closed-form expression of the joint probability density function of two polarimetric data thus enabling the exact evaluation of the change detection performances. Regarding the proposed temporal polarimetric data distribution, we propose a new algorithm for evaluating the change detection with KL-divergence test. The KL-divergence is a distance measurement between two probability distributions. In our case, also the case of mutual information, it measures the dependency of two variables by calculating the distance between the probability density of joint distribution of polarimetric data and their marginal probability densities. We illustrate this new change detection algorithm is independent from the dimension of the system that it can be easily implemented to lower or higher multi-channel SAR systems.