IEEE Geoscience and Remote Sensing Magazine - December 2021 - 251

the spectral library. Furthermore, databases containing
laboratory-acquired spectra often contain hundreds of different
materials. Using a library of this size can actually decrease
the performance of SU since the problem becomes
more and more ill-posed. One solution consists of removing
redundant and irrelevant signatures from large spectral
libraries before the SU process. These approaches, which
are also called library pruning, have been largely applied to
reduce the complexity and improve the accuracy of MESMA
[38] and sparse unmixing algorithms [292]. There are
three main groups of library pruning techniques. Library
reduction approaches remove only redundant signatures
to improve the computation time. EM selection techniques
identify which materials are present in each hyperspectral
image pixel to remove absent EM classes from the library
before SU. Same-class library pruning attempts to identify
and remove signatures that are acquired in different conditions
from those of the observed image. These approaches
are reviewed in detail in the following.
LIBRARY REDUCTION TECHNIQUES
SPECTRAL LIBRARY REDUCTION
Spectral library reduction involves the following:
◗ It employs very simple strategies that do not depend on the observed
hyperspectral image.
◗ It reduces computational complexity but does not improve the quality
of the SU results.
Library reduction techniques attempt to remove redundant
spectral signatures, regardless of the observed hyperspectral
image, which tends to improve the computational
complexity of SU but not necessarily its quality. A common
idea is to find a small set of signatures that can best represent
the remaining spectra of the same EM class in some
sense [293], such as the squared error [38], average spectral
angle [89], and count-based EM selection metric, where
one counts the number of signatures that one candidate
can represent with an error below a threshold [93]. An alternative
method divided the library signatures into groups
according to their Euclidean norm, selecting one signature
from each group to explicitly account for brightness variations
[294].
ENDMEMBER SELECTION METHODS
ENDMEMBER SELECTION
For EM selection, the following must be considered:
◗ It can remove only entire material classes from the library for each
pixel; it is also effective for variability-free SU.
◗ It can leverage information from the observed hyperspectral image.
◗ It can improve SU quality and reduce computational complexity.
◗ It usually depends on some sort of classification procedure.
◗ It relies on the observation that only a few materials are normally
contained in each pixel.
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
Recent approaches proposed to remove signatures from
the library that were acquired in conditions that differed from
those of the hyperspectral image, keeping only signatures that
were representative of the observed image. However, measuring
the representativeness of EM signatures is a difficult task.
A simple approach suggested removing signatures that have
a large spectral angle and spectral L1
distance relative to the
observed pixels [303]. However, this strategy might discard
relevant signatures in the presence of many mixed pixels. Another
work proposed to compare only pure pixels extracted
from the image with the library spectra in the wavelet domain
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EM selection techniques attempt to identify which EM
classes are present in each pixel by using information, such
as classification maps [10], [295], to remove absent materials
from the library and improve the unmixing results [10],
[295]. This relies on the observation that hyperspectral image
pixels usually contain only a small number of materials,
and it has also been applied to SU without considering
spectral variability [296], [297]. The simplest EM selection
methods use classification algorithms to select the EM classes
present in mixed pixels [298], [299]. Another work employed
a block sparse unmixing algorithm as a preprocessing step
to remove material classes with low abundance values from
the library for each image pixel before applying the MESMA
algorithm to obtain the final SU results [300]. A more elaborate
approach proposed to semantically organize subsets of
material classes in a hierarchical tree, starting from a rough
(e.g., pervious and impervious) differentiation and progressing
to a fine one between the EMs (e.g., different vegetation
species) [59]. Afterward, SU was performed at each level of
the tree, using the abundance results in the previous, coarser
level to constrain which EMs could be selected at the current
one (i.e., a pixel containing only a pervious EM in the coarse
scale cannot have a concrete EM in the finer one).
Some recent approaches have proposed to use external
complementary data to aid in identifying which materials
are present in each pixel. For instance, in [301], the hyperspectral
image was divided into rural and urban subsets
using external data about road network density, which enabled
the use of a separate set of EM classes for each of the
subsets. Another work proposed to use additional lidar data
to remove material classes from the library of each pixel,
based on its height distribution (e.g., a " tree " or " building "
EM can be removed from a pixel that has low height) [302].
PRUNING LIBRARIES WITHIN THE SAME CLASS
SAME-CLASS ENDMEMBER PRUNING
This process has the following qualities:
◗ It can remove spectral signatures from each material class that are not
representative of the observed hyperspectral image.
◗ It can improve the SU quality and reduce the computational cost, even
for libraries with few material classes.
◗ Identifying which signatures in the spectral library do not share acquisition
conditions with the observed image is generally difficult.
IEEE Geoscience and Remote Sensing Magazine - December 2021

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