Object Characterization from Spectral Data Using Nonnegative Factorization and Information Theory

Abstract

The identification and classification of non-imaging space objects, and ultimately the determination of their shape, function, and status, is an important but difficult problem still to be resolved. While ground-based telescopes with adaptive optics technology have been able to produce high-resolution images for a variety of spaced-based objects, current telescope technology is limited for objects in orbits beyond 1,000 km altitude, such as geosynchronous satellites (approx. 36,000 km orbit). An interesting and promising approach to circumvent this limitation is to collect wavelength-resolved spectral reflectance data, rather than spatially-resolved data, which can then be used to determine information such as material composition of an object. Current work has been focused on the determination of material composition (fractional abundances) from spectral traces when the types or classes of composing materials are known a priori. In this paper, we extend previous work to determine not only fractional abundances, but also the classes of composing materials that make up the object, called endmembers. Endmembers are selected using information-theoretic methods. We employ non-negative matrix factorization algorithms for unmixing of spectral reflectance data to find endmember candidates and regularized inverse problem methods for determining corresponding fractional abundances. Promising numerical results are presented using laboratory and simulated datasets.