IEEE Geoscience and Remote Sensing Magazine - December 2021 - 250

avoid the inclusion of pixels extracted from mixed homogeneous
regions in the library.
Some alternatives tried to build spectral libraries by using
different forms of the matrix factorization of the hyperspectral
image. For instance, spectral libraries for each material
class are constructed in [193] by learning sparse representations
of sets of pure pixels of each material, which are extracted
from the observed image. More precisely, dictionary
learning is applied to the pure pixels of each material, from
which the resulting basis matrices are used to construct the
spectral library. Another approach proposed to extract the
spectral library using the results of an SU procedure employing
a matrix factorization approach, which does not account
for spectral variability [277]. However, besides depending
on the results of another SU algorithm, there is no guarantee
that the selected signatures are pure pixels.
GENERATING SPECTRAL LIBRARIES
FROM PHYSICS MODELS
PHYSICS-BASED LIBRARY SYNTHESIS
Physics-based library synthesis has the following qualities:
◗ It can generate libraries independently of the observed image.
◗ It can represent a wide range of spectral variability if more complex
models are employed.
◗ It depends on the availability of an accurate physical model for the
EM spectra.
An alternative approach to generate spectral libraries
that does not depend on the observed hyperspectral image
is to employ a physics-based (i.e., radiative transfer)
model describing the reflectance of the EMs as a function
of physicochemical parameters. This enables us to generate
different instances of the material spectra to constitute
a synthetic library by sampling the free parameters of
the model. Examples of such representation include the
PROSPECT model [69] for vegetation and Hapke's [48] and
Shkuratov's models [196] for packed particle spectra. Different
representations inspired by physics have been employed
to generate and augment spectral libraries for SU in
many applications, which include describing tree canopy
as a function of its height and radius [279], fire temperature
radiance as a function of the view and solar geometry
and atmospheric conditions [280], and soil reflectance as
a function of moisture content [73]. This strategy has also
been applied to generate training data for the SU of binary
mixtures of vegetation and impervious materials through
machine learning algorithms [281]-[284]. Note, however,
that directly sampling all parameters of complex models,
such as PROSPECT, might lead to a very large number of
signatures. This has motivated strategies to sample the
parametric models more efficiently and to remove redundant
spectra from the generated library [285].
Despite their advantages, a significant drawback of
these methods is the requirement for accurate knowledge
of the physical process governing the observation of the
250
reflectance of the materials by the sensor. A different approach
attempted to circumvent this issue by proposing a
data augmentation strategy, where one wishes to synthesize
additional signatures to be included in small, preexisting libraries
[286]. The spectral signatures in the library are used
as training data to learn the statistical distribution of the
EMs through deep generative models, such as variational
autoencoders and deep neural networks. This enables one
to sample new signatures from the learned distributions to
augment the existing library.
SPATIAL INTERPOLATION OF ENDMEMBER
SIGNATURES
SPATIAL ENDMEMBER INTERPOLATION
For spatial EM interpolation, the following is true:
◗ The process uses the hypothesis of spatially correlated EM signatures.
◗ It needs knowledge of the spatial position of pure pixels in the scene.
◗ The number of available pure pixels can strongly affect the performance
of the methods.
A number of approaches based on the assumption that
EMs are spatially correlated have proposed to synthesize
pixel-dependent EM signatures based on a set of pure
pixels at known spatial locations through interpolation
techniques. Many of these works aim to perform the SU
of vegetation and soil mixtures by employing vegetation
indices (i.e., spectral features given by ratios of band differences,
such as the NDVI) in lieu of traditional EMs. For
instance, the spatial interpolation of vegetation and soil
NDVIs based on linear regression has been considered
for the SU of coarse-resolution images, where the training
samples for the EMs were obtained using classification
maps from complementary high-resolution images available
a priori [287].
A similar strategy considered the use of spatially
weighted kriging employing as training samples pure pixels
that were manually extracted from the scene [288] or
obtained by randomly sampling the vertices of the simplex
obtained by a low-dimensional projection of the
hyperspectral image [289]. This strategy enabled one to
weight the contribution of the training samples according
to their spatial distance to each interpolated signature.
Other works considered the spatial interpolation of actual
spectral signatures, instead of just vegetation and soil
indices, by using spatially weighted linear regression or
kriging. This has been performed by considering training
data obtained from complementary high-resolution classification
maps [290] and pure pixels extracted from the
image inside subregions that were selected with the aid of
a classification algorithm [291].
LIBRARY PRUNING TECHNIQUES
One significant problem with many SU methods based
on spectral libraries, such as MESMA, is that their computational
complexity increases quickly with the size of
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2021
IEEE Geoscience and Remote Sensing Magazine - December 2021

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