IEEE Geoscience and Remote Sensing Magazine - December 2021 - 228

extraction and pruning methods as well as the approaches'
main characteristics.
EXPERIMENTAL ASPECTS AND TOOLBOX
The practical aspects related to the evaluation of SU methods
when spectral variability is considered are also discussed
in the " Experimental Evaluation " section. This
includes the generation of realistic synthetic data and a
list of existing software resources that are available to the
reader. We also present a simulation to demonstrate the
application of a few of the SU techniques reviewed in the
article, which were chosen by selecting different paths in
the proposed decision tree. This example is made publicly
available in the form of a software toolbox at https://
github.com/ricardoborsoi/ unmixing_spectral_variability
and in [13].
ORIGINS OF SPECTRAL VARIABILITY
AND ITS EFFECTS
The variability in spectral signatures occurs mainly due to
1) atmospheric effects, 2) illumination and topographic
changes, and 3) the intrinsic variation of the spectral signatures
of the materials (i.e., due to physicochemical differences).
Understanding how these conditions affect the
spectral signatures of the materials and the unmixing results
is important for the development of informed models
and methods to deal with EM variability. Such knowledge
can be used, for instance, to generate physics-based and
physically inspired models that include the effects of spectral
signature variability. Such representations can then be
directly incorporated into the SU process (as discussed in
the " Parametric Models " section) and used to generate synthetic
spectral libraries for library-based SU (as discussed
in the " Generating Spectral Libraries From Physics Models "
section).
In addition to SU, spectral variability affects other hyperspectral
imaging tasks, which prompted extensive investigations
into its causes and how it manifests in material
spectra. In this context, a recent review article by Theiler
et al. [14] provides an excellent overview of spectral variability
in hyperspectral target detection. In particular, the
causes and effects of spectral variability in target detection
are reviewed, with a focus on the study of environmentally
induced variability (caused by, e.g., atmospheric and
topographic changes) through an in-depth examination
of radiative transfer models. A detailed computer simulation
is included to illustrate how the material spectra
are affected by changes in the parameters of the radiative
transfer model.
In the following, we review the causes and effects of
spectral variability from an SU perspective. Although we
also introduce the radiative transfer function interpretation
of some atmospheric and topographic effects, we
focus our exposition on a more generic analysis of the
consequences that spectral variability has for the observed
pixel spectra and on the results of SU as reported
228
by previous experimental works (i.e., with a stronger focus
on the results of, e.g., atmospheric compensation methods
as opposed to the interpretation of the imaging models
themselves). The interested reader can find a more comprehensive
analysis from a radiative transfer function
standpoint in [14].
ATMOSPHERIC EFFECTS
One of the main sources of spectral variability is atmospheric
interference when measuring ground reflectance.
Atmospheric gases (such as ozone, oxygen, methane,
carbon dioxide, and so on), aerosols, and, most prominently,
water vapor absorb significant amounts of radiation,
while other molecules and vapors scatter incoming
light [15]. These effects have an impact on the radiance
measured at the sensor, which can become significantly
different than that corresponding to the desired ground
reflectance. Atmospheric absorption from gases is also
heavily wavelength dependent, whereas aerosol absorption
varies smoothly in spectra. These effects must be
compensated for to achieve an accurate characterization
of surface reflectance.
Atmospheric compensation models can be roughly divided
into statistical (empirical) and physics-based varieties
[15]. Statistical models are based on additional information
about the atmospheric influence, usually obtained
by means of reference objects and calibration panels in
the scene. This information is used to find a relationship
(e.g., linear) between the radiances observed at the sensor
and at the surface of the scene [15]. This results in gain
and offset factors for each spectral band, which are then
uniformly applied to every image pixel to compensate for
the atmospheric effects [15]. Sometimes, when a reference
object is not present in the scene, naturally occurring
objects can be employed, most commonly consisting
of smooth bodies of water, which exhibit low reflectance
and can be considered dark objects [5]. The downsides of
this approach are 1) the true reflectance of a reference object
must be accurately known, and 2) it does not account
for the spatial variability of the distribution of gases and
aerosols. This variability can be very significant, and thus
it can introduce spatially dependent residual atmospheric
effects. A classic example of statistical methods is the empirical
line method [5].
Physics-based models, on the other hand, are robust
alternatives to empirical methods and do not assume that
additional information about the scene is known. These
methods are mature and widely used, addressing the limitations
of empirical approaches by employing a rigorous
model that explicitly describes the absorption and scattering
effects due to atmospheric gases and aerosols [16]. Popular
examples include the atmospheric removal algorithm
and the Fast Line-of-Sight Atmospheric Analysis of Spectral
Hypercubes (FLAASH) [15].
Assuming ground terrain illuminated by the sun,
the light incident on a pixel in the sensor can be roughly
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2021
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IEEE Geoscience and Remote Sensing Magazine - December 2021

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