Object Characterization from Spectral Data Using Nonnegative Factorization and Information Theory J. Piper * V. Paul Pauca † Robert J. Plemmons ‡ Maile Giffin § Abstract The identification and classification of non-imaging space objects, and ultimately the deter- mination 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 pro- duce 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. 1 Introduction The determination of space objects whose orbits are significantly distant (e.g. geosynchronous satellites) or whose dimensions are small (e.g. nanosatellites) is a challenging problem in astro- nomical imaging. Because of their distant orbits or small dimensions these objects are difficult to resolved spatially using ground-based telescope technology, hence they are denoted as non-imaging objects (NOI). Recently alternate approaches have been proposed in an attempt to circumvent this problem. Among these, the collection and analysis of wavelength-resolved data is a promising and * Department of Computer Science, Wake Forest University, Winston-Salem, NC 27109. His research was supported in part by the Air Force Office of Scientific Research under grant F49620-02-1-0107. Email: pipejw02@wfu.edu † Department of Computer Science, Wake Forest University, Winston-Salem, NC 27109. His research was supported in part by the Air Force Office of Scientific Research under grant FA49620-03-1-0215, and by the Army Research Office under grant DAAD19-00-1-0540. Email: paucavp@wfu.edu ‡ Departments of Computer Science and Mathematics, Wake Forest University, Winston-Salem, NC 27109. His research was supported in part by the Air Force Office of Scientific Research under grant F49620-02-1-0107 and by the Army Research Office under grant DAAD19-00-1-0540. Email: plemmons@wfu.edu § Oceanit Laboratories, 590 Lipoa Parkway Kihei, Maui, HI 96753. Her research was supported in part by the Air Force Office of Scientific Research under grant F49620-02-1-0107. Email: mgiffin@oceanit.com 1