Schrodinger Eigenmaps for Spectral Target Detection

Spectral imagery such as multispectral and hyperspectral data could be seen as a set of panchromatic images stacked as a 3d cube, with two spatial dimensions and one spectral. For hyperspectral imagery, the spectral dimension is highly sampled, which implies redundant information and a high spectral dimensionality. Therefore, it is necessary to use transformations on the data not only to reduce processing costs, but also to reveal some features or characteristics of the data that were hidden in the original space. Schrodinger Eigenmaps (SE) is a novel mathematical method for non-linear representation of a data set that attempts to preserve the local structure while the spectral dimension is reduced. SE could be seen as an extension of Laplacian Eigenmaps (LE), where the diffusion process could be steered in certain directions determined by a potential term. SE was initially introduced as a semi supervised classification technique and most recently, it has been applied to target detection showing promising performance. In target detection, only the barrier potential has been used, so different forms to define barrier potentials and its influence on the data embedding are studied here. In this way, an experiment to assess the target detection vs. how strong the influence of potentials is and how many eigenmaps are used in the detection, is proposed. The target detection is performed using a hyperspectral data set, where several targets with different complexity are presented in the same scene.