February Fourier Talks 2014

Automated extraction of quantitative information via detection algorithms from remotely sensed multi- & hyperspectral imagery requires one to have a mathematical model for the "background" and "foreground" signatures in the image. Given these data models, one can then make decisions per-pixel as to the likelihood of the presence of a signature of interest. Traditional processing schemes rely heavily on simple first and second order statistics or linear subspace models of the data to make these decisions and have been successful in several applications such as sub-pixel target detection and anomaly detection. However, the new generation of sensors has a significant improvement in spatial and spectral coverage and resolution. At these improved spatial and spectral resolutions, the sensors image the surface of the Earth at ever-greater levels of detail. It is simple to show that assumptions of multivariate normality, or that the data are well-defined by linear subspaces, are not well-met by the current generation of sensors. Here we will present methods that derive from a graphical model of the image data in the spectral domain. Non-linear dimensionality reduction methods have been widely applied to hyperspectral imagery due to its structure as the information can be mapped in a lower dimensional subspace. One of these methods is Laplacian Eigenmaps (LE), which has been widely used in clustering or automated classification. Schrodinger Eigenmaps (SE) has been previously introduced as a semi-supervised classification scheme in order to improve the classification performance by taking advantage of labeled data, encoded in a potential term V. Here, we explore the idea of using SE in target detection by varying V to include target signature label data. Experimental results using different targets are shown.