International Journal of Applied Earth Observation and Geoinformation 26 (2014) 387–398 Contents lists available at ScienceDirect International Journal of Applied Earth Observation and Geoinformation jo ur nal home page: www.elsevier.com/locate/jag A spatial–spectral approach for deriving high signal quality eigenvectors for remote sensing image transformations Derek Rogge a,∗ , Martin Bachmann a , Benoit Rivard b , Allan Aasbjerg Nielsen c , Jilu Feng b a German Remote Sensing Data Centre, DLR, Munchnerstr. 20, D-82234, Germany b Department of Earth and Atmospheric Sciences, University of Alberta, Edmonton T6G 2E3, Canada c Technical University of Denmark, National Space Institute, DK-2800 Kgs. Lyngby, Denmark a r t i c l e i n f o Article history: Received 3 July 2013 Accepted 13 September 2013 Keywords: Hyperspectral imaging Spatial and spectral processing Eigenvector transformations a b s t r a c t Spectral decorrelation (transformations) methods have long been used in remote sensing. Transformation of the image data onto eigenvectors that comprise physically meaningful spectral properties (signal) can be used to reduce the dimensionality of hyperspectral images as the number of spectrally distinct signal sources composing a given hyperspectral scene is generally much less than the number of spectral bands. Determining eigenvectors dominated by signal variance as opposed to noise is a difficult task. Problems also arise in using these transformations on large images, multiple flight-line surveys, or temporal data sets as computational burden becomes significant. In this paper we present a spatial–spectral approach to deriving high signal quality eigenvectors for image transformations which possess an inherently abil- ity to reduce the effects of noise. The approach applies a spatial and spectral subsampling to the data, which is accomplished by deriving a limited set of eigenvectors for spatially contiguous subsets. These subset eigenvectors are compiled together to form a new noise reduced data set, which is subsequently used to derive a set of global orthogonal eigenvectors. Data from two hyperspectral surveys are used to demonstrate that the approach can significantly speed up eigenvector derivation, successfully be applied to multiple flight-line surveys or multi-temporal data sets, derive a representative eigenvector set for the full image data set, and lastly, improve the separation of those eigenvectors representing signal as opposed to noise. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Most airborne hyperspectral systems today typically comprise 100’s of contiguous bands ranging from 0.4 to 2.5 m and produce significant quantities of data, commonly 100’s of megabits in size. With the advent of satellite hyperspectral sensors (e.g. Hyperion (Pearlman et al., 2001), EnMap (Stuffler et al., 2007), PRISMA and HyspIRI (Buckingham and Staenz, 2008), HISUI (Kawashima et al., 2010)), the amount of data available for analysis increases sub- stantially. Processing this type of data, from acquisition through to map generation, requires numerous computationally intensive steps (e.g. radiometric correction, atmospheric correction, geomet- ric correction, classification, validation). Thus, there is a real need to develop cost-effective algorithm implementations to satisfy time- critical remote sensing applications (Plaza et al., 2009) that also produce quality, physically accurate results that the end user can ∗ Corresponding author. Tel.: +49 8153283364; fax: +49 8153281458. E-mail addresses: derek.rogge@dlr.de (D. Rogge), martin.bachmann@dlr.de (M. Bachmann), benoit.rivard@ualberta.ca (B. Rivard), aa@space.dtu.dk (A.A. Nielsen), jfeng@ualberta.ca (J. Feng). use in specific applications (Rogge et al., 2012). Improvements in computing power, memory, parallel processing and advancing existing algorithms for more efficient processing of large data sets can help to achieve these needs. However, any improvements with respect to reducing computational load must be done such that there is little, or preferably no, loss in quality. Spectral decorrelation (transformations) methods have long been used in remote sensing, such as principal component analysis (PCA) (Ready and Wintz, 1973; Singh and Harrison, 1985), maxi- mum noise fraction (MNF) (Green et al., 1988) and singular value decomposition (SVD) (Danaher and O’Mongain, 1992), which are all based on strong mathematical foundations. Uses include pre- and post-processing steps, such as data compression (Du et al., 2009), correcting for spectral smile effects (Dadon et al., 2010), eigenvector based approaches to virtual dimensionality (VD) estimation (Chang and Du, 2004), or endmember extraction (Boardman et al., 1995). Transformations are commonly used to reduce the dimensional- ity of hyperspectral images as the number of spectrally distinct signal sources composing a given hyperspectral scene is generally much less than the number of spectral bands. Transformation of the image data onto eigenvectors can give a user quick results that show the spatial distribution of the majority of spectrally distinct 0303-2434/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jag.2013.09.007