Spatial-spectral operator theoretic methods for hyperspectral image classification
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Spatial-spectral operator theoretic methods for hyperspectral image classification John J. Benedetto1 · Wojciech Czaja1 · Julia Dobrosotskaya2 · Timothy Doster1 · Kevin Duke3
Received: 30 May 2016 / Accepted: 22 June 2016 © Springer-Verlag Berlin Heidelberg 2016
Abstract With the emergence of new remote sensing modalities, it becomes increasingly important to find novel algorithms for fusion and integration of different types of data for the purpose of improving performance of applications, such as target/anomaly detection or classification. Many popular techniques that deal with this problem are based on performing multiple classifications and fusing these individual results into one product. In this paper we provide a new approach, focused on creating joint representations of the multi-modal data, which then can be subject to analysis by state of the art classifiers. In the work presented in this paper we consider the problem of spatial-spectral fusion for hyperspectral imagery. Our approach involves machine learning techniques based on analysis of joint data-dependent graphs and the resulting data-dependent fusion operators and their representations. Keywords Manifold learning · Hyperspectral · Spatial-spectral fusion Mathematics Subject Classification 42C99
1 Introduction Hyperspectral imaging (HSI) is among the most significant developments in remote sensing in the recent years. The technology, at its core, recovers radiation reflected
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Wojciech Czaja [email protected]
1
Department of Mathematics, University of Maryland, College Park, MD, USA
2
Department of Mathematics, Case Western Reserve University, Clevland, OH, USA
3
Department of Mathematics and Statistics, American University, Washington, DC, USA
123
Int J Geomath
from the surface of objects across many wavelengths and has a wide range of practical applications, ranging from agriculture, through mineralogy and exploration to applications in the security and defense fields. Farmers are able to utilize hyperspectral images to determine plant stress levels, amount of water being absorbed, and possible insect infestations (Thenkabail et al. 2000). In resource exploration, in particular in mineralogy exploration, hyperspectral images can be quickly obtained for a vast amount of territory and then known spectral signatures corresponding to desirable minerals can be searched for Meer (2004). The defense industry makes wide use of hyperspectral images for target detection and tracking (Manolakis et al. 2003) because, for example, the limitations of the human vision make it difficult to discern modern camouflage from vegetation (Schaum and Stocker 2004). From a mathematical perspective, a hyperspectral image with hundreds of spectral bands is a far reaching generalization of a standard digital image which has only three spectral bands. Thus, it offers a more complete representation of the light spectrum for viewing and analysis. A regular color image can be interpreted as a collection of three-dimensional spectral vectors, each representing th
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