Novel Approach for Assessing Uncertainty Propagation via Information-Theoretic Divergence Metrics and Multivariate Gaussian Copula Modeling

With all of the new remote sensing modalities available, with ever increasing capabilities, there is a constant desire to extend the current state of the art in physics-based feature extraction and to introduce new and innovative techniques that enable the exploitation within and across modalities, i.e., fusion. A key component of this process is finding the associated features from the various imaging modalities that provide key information in terms of exploitative fusion. Further, it is desired to have an automatic methodology for assessing the information in the features from the various imaging modalities, in the presence of uncertainty. In this paper we propose a novel approach for assessing, quantifying, and isolating the information in the features via a joint statistical modeling of the features with the Gaussian Copula framework. This framework allows for a very general modeling of distributions on each of the features while still modeling the conditional dependence between the features, and the final output is a relatively accurate estimate of the information-theoretic J-divergence metric, which is directly related to discriminability. A very useful aspect of this approach is that it can be used to assess which features are most informative, and what is the information content as a function of key uncertainties (e.g., geometry) and collection parameters (e.g., SNR and resolution). We show some results of applying the Gaussian Copula framework and estimating the J-Divergence on HRR data as generated from the AFRL public release data set known as the Backhoe Data Dome.