Detection & Instrument Characterization Using Spatial Statistical Models

Statistical modeling is a crucial piece of the imaging spectroscopy estimation and detection pipeline. Specifically, recovery of surface reflectance by optimal estimation techniques relies on an accurate assessment of the noise covariance for each sensor. Furthermore, the accuracy of existing detection techniques (e.g., matched filters) largely depends on a faithful reconstruction of the statistics of the scene such as the underlying covariance matrix. For push-broom imaging instruments (e.g., Aviris NG), two challenges arise in estimating a representative covariance matrix: a) the spatial continuity of scenes implies that observed samples are highly correlated and should not be treated as independent, and b) the observed spectra in the cross-track direction come from different sensors having separate noise distributions. Existing approaches address these challenges by applying an ad-hoc preprocessing step to de-correlate the samples, and then calculate a separate covariance matrix for each cross-track element. In this work, we propose a principled statistical graphical modeling approach that characterizes inter-dependencies across samples gathered by the same detector, as well as the intra-dependencies across different detectors; these dependencies are encoded via a few parameters in a sparsely constrained covariance model. In contrast to existing methods, this approach can accommodate multiple detector information, leading to a larger effective sample size and ultimately a more accurate covariance estimate. Further, the structured covariance matrix can be computed efficiently via a convex optimization program. We use imaging spectroscopy datasets to demonstrate that our statistical procedure yields a more faithful model as compared to previous techniques, and explore what these discrepancies imply with respect to signature detection.