IEEE Geoscience and Remote Sensing Magazine - June 2013 - 7

and spectral resolution instruments (see [3] and references therein).
Figure 1 gives a partial account of the relevance of
hyperspectral applications, by comparing paper counts
per year in the hyperspectral and radar areas. These results
were obtained by searching the SCI-Expanded database of
the ISI Web-Of-Science with the topics "(hyperspectral)
and (remote sensing)," in the left hand side, and "(radar)
and (remote sensing)," in the right hand side. We conclude
that the number of items per year in 2011 is similar for the
hyperspectral and radar areas, with a clear increasing trend
in the former and a stabilization or decrease in the latter.
In hyperspectral imaging, also termed imaging spectroscopy [4], the sensor acquires a spectral vector
with hundreds or thousands of elements from
every pixel in a given scene. The result is
the so-called hyperspectral image
(HSI). It should be noted that HSIs
are spectrally smooth and spatially piece-wise smooth: the
values in neighboring locations and wavelengths
are highly correlated.
This can be observed
by extremely nondiagonal covariance
matrices and wide
autocorrelation functions [1]. This piecewise
smoothness
holds as well in the
spatio-spectral direction. The characteristics
are similar to those of natural photographic images
and videos and, therefore,
many tools that were developed
for these data can be extended for
HSI analysis.
An equivalent interpretation of an HSI
is given by the acquisition of a stack of images
representing the radiance in the respective band
(wavelength interval). Due to this interpretation, the HSIs
are also termed hyperspectral data cubes. These two points
of view are illustrated in the top left hand side of Fig. 2,
where the HSI has n b spectral bands and n 1 # n 2 pixels. The
plots on the top right hand side show the spectra of pixels
containing soil, vegetation, and water. Owing to the high
spectral sampling, the spectral information is often highly

correlated and thus lives in a low dimensional manifold.
This is illustrated at the bottom of Fig. 2, where the spectral
vectors of soil, vegetation, and water are represented as R nb
dimensional points on a surface.
In terms of the geometrical properties of a remote sensing imaging system, the spatial resolution of a sensor is
given by its field of view (FOV), and the obtained spectrum
is the average of the material's reflectances within this FOV.
The spectral resolution is determined by the bandwidth
of the spectral bands. When spatially and spectrally sampling the information (we will assume that the sampling is
performed at the sensors spatial and spectral resolution),
a 3D "hypercube" X ! R n 1 # n 2 # n b is obtained, containing
n = n 1 # n 2 pixels and n b bands (see Fig. 2). Different forms
of representation can be used for HSIs:
◗ In the spectral representation, each pixel is defined in
the spectral space x ! R n b. Since neighboring spectra correspond to similar materials, grouping in this spectral
space is commonly applied to characterize materials.
This can be done by clustering neighboring spectra, or
by supervised classification (see section on Classification). Since the spectral correlation is high, the data are
likely to reside on a very low-dimensional submanifold
of the spectral space, and projection of the data on a subspace of dimension d % n b, using, e.g., principal component analysis (PCA) [3], is commonly applied.
◗ In the spatial representation, each image band is a
matrix X i ! R n 1 # n 2. Because of the high spatial correlation, neighboring pixels are likely to belong to a similar material and spatial grouping (e.g., segmentation) is
commonly applied.
◗ In the spatial-spectral representation spectral processing
of a pixel is performed taking neighboring pixels into
account, while spatial processing of an image band is
performed by accounting for the other bands.
These representations have been actively exploited,
namely, in dimensionality reduction, feature extraction,
unmixing, classification, segmentation, and detection [1],
[5]. Still related with the high dimensionality of the spectral
information, the most recent trend is sparse and redundant
modeling, which is currently reaching the areas of, e.g.,
restoration, unmixing, classification, segmentation, and
detection (see, e.g., [6], [7] and references therein).
Since the output of a hyperspectral sensor provides raw
digital number (DN) values and for quantification purposes, a conversion to apparent surface reflectance values
is required before using advanced information extraction
techniques such as those mentioned above [8]. The characteristics of the sensor itself are described by its transfer

José M. Bioucas-Dias is with the Instituto de Telecomunicações, Instituto Superior Técnico, Lisbon, 1049-1, Portugal (e-mail: bioucas@lx.it.pt). Antonio
Plaza is with the Hyperspectral Computing Laboratory, Department of Technology of Computers and Communications, Escuela Politécnica de Cáceres,
University of Extremadura, 10003 Cáceres, Spain (e-mail: aplaza@unex.es). Gustavo Camps-Valls is with the Image Processing Laboratory, Universitat de
València, C/Catedrático Escardino, E-46980 Paterna (València), Spain (e-mail: gustavo.camps@uv.es). Paul Scheunders is with iMinds, Vision Lab, Department of Physics, University of Antwerp, 2610 Wilrijk, Belgium (e-mail: paul.scheunders@ua.ac.be). Nasser Nasrabadi is with the U.S. Army Research Laboratory, Adelphi, MD 20783 USA (e-mail: nasser.m.nasrabadi.civ@mail.mil). Jocelyn Chanussot is with the GIPSA-Lab, Grenoble Institute of Technology,
Grenoble, France (e-mail: jocelyn.chanussot@gipsa-lab.grenoble-inp.fr). This work was supported by the Portuguese Science and Technology Foundation,
project PEst-OE/EEI/0008/2013 and by the Spanish Ministry of Economy and Competitiveness (MINECO) under projects TIN2012-38102-C03-01 and
AYA2011-29334-C02-02.
june 2013

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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2013