IEEE Geoscience and Remote Sensing Magazine - December 2021 - 255

observed image, as described in greater detail in the following
section. The spectral libraries were also used to estimate
the parameters of the beta distribution in the BCM. The regularization/tuning
parameters of the algorithms (fractional
sparse SU, ELMM, DeepGUn, and RUSAL) were manually
adjusted to maximize the abundance reconstruction performance
measured in an independent data set generated
following the specifications at the beginning of the " Experimental
Setup and Results " section.
LIBRARY EXTRACTION
To demonstrate the use of library-based SU methods in
practical settings, the spectral libraries used by MESMA
and fractional sparse SU were extracted directly from the
observed image. We used the method described in [267],
which consists of performing EM extraction (in this case,
using the VCA algorithm) in subsets of pixels randomly
sampled from the image. We extracted five sets of EMs,
using subsets of 500 pixels each (sampled with replacement).
The library was kept small to prevent the inclusion
of redundant signatures and reduce the probability of selecting
mixed pixels by mistake. As a byproduct, this kept
the computational complexity of methods such as MESMA
very low, while providing good experimental results. The
estimated signatures can be viewed in Figure 17. Although
the spectral variability in Figure 17 is less accentuated than
that of the true EMs in Figure 16, the estimated signatures
are good representatives of the materials in the scene. The
good performance of the library extraction method can be
explained by the presence of multiple pure pixels in the
synthetically generated abundance maps, as evident in the
first row of Figure 18.
DISCUSSION
The quantitative results are provided in Table 4, while the
estimated abundance maps and EMs are depicted in Figures 18
and 19, respectively. Note that the RMSEM
and SAMM
are
not available for FCLS, RUSAL, NCM-E, and BCM since
0.1
0.2
0.3
0.4
0.5
0.5 1 1.5 2
(a)
Wavelength (µm)
0.1
0.3
0.5
0.7
0.9
0.5 1 1.5 2
(b)
Wavelength (µm)
FIGURE 17. EM bundles extracted by batch VCA [267] for (a) vegetation, (b) soil, and (c) water.
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
255
these algorithms do not estimate the spectral signatures of
the EMs present in each pixel of the image. All methods
that considered spectral variability led to better abundance
reconstruction results than the FCLS baseline. In particular,
the library-based methods (MESMA and fractionalbased
sparse SU) had very good performance, which likely
occurred due to the image-extracted spectral library accurately
representing the typical EM variability contained in
the scene. Moreover, sparse SU with fractional norms performed
similarly and slightly better than MESMA.
The methods based on parametric EM models (ELMM
and DeepGUn) also led to considerable improvements
when compared to FCLS, especially considering that the
EMs were estimated directly from the image. The EMmodel-free
method (RUSAL), which takes general variability
and incorrect models into account, also provided
an improvement over FCLS, albeit smaller when compared
to ELMM and DeepGUn. However, the sensitivity of these
techniques to the selection of the regularization parameters
can negatively impact their performance when Monte
Carlo simulations are considered.
Among the Bayesian methods (NCM-E and BCM), BCM
provided a considerable performance improvement over
FCLS, especially when taking into account the unsupervised
nature of the method (i.e., no parameter has to be
adjusted). The NCM-E results, on the other hand, were virtually
identical to those of FCLS, which indicates that the
isotropic Gaussian EM hypothesis may not be appropriate
for this data set. The performance of the different methods
can be visually distinguished in Figure 18, especially from
the soil EM, in which the similarity between the reconstructions
and the reference abundance maps reflects the
general behavior of the quantitative results from Table 4.
The EM reconstruction metrics in Table 4 indicate that
the EMs selected by library-based approaches (MESMA and
fractional sparse SU) are close to the reference ones, especially
in terms of
SAMM while the model-based approach,
es
(ELMM and DeepGUn) provided slightly worse results,
0.15
0.1
0.05
0.51 1.5 2
(c)
Wavelength (µm)
Reflectance
Reflectance
Reflectance

IEEE Geoscience and Remote Sensing Magazine - December 2021

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