IEEE Geoscience and Remote Sensing Magazine - December 2021 - 241

techniques attempted to reduce the need for user supervision
in the process. For instance, EM extraction and SU
were performed individually in local (square) image tiles
in [174] and [175]. Afterward, the locally extracted EMs
and abundance maps were merged into the global EM sets
and abundance maps using clustering algorithms. Image
segmentation methods were later applied to provide more
flexibility when dividing the hyperspectral image into local
regions. For instance, in [176], manual EM extraction
and SU (using the FCLS algorithm) were individually performed
in each image region defined by a segmentation
algorithm. Another work considered a superpixel decomposition
of the image, aided by external map metadata
to compute a more accurate segmentation [177]. A more
sophisticated method proposed in [178] and [179] used
a binary partition tree to divide the image into different
regions, from a coarse to a fine spatial scale. Local unmixing
was then performed at the scale of the partition tree
that yielded the smallest REs.
Besides the choice of the segmentation procedure, EM
extraction is a challenging part of local unmixing and has
a great impact on the performance of these algorithms.
A spatially adaptive unmixing method was proposed in
[180] to estimate the distribution of different surfaces in
urban environments. EM spectra for each pixel were synthesized
as a weighted average of pure pixels extracted in
a spatial neighborhood specified by the user, with weights
given as a function of their distance to each mixed pixel
at hand. A similar approach employed as EMs the mean
values of pure pixels extracted within each (square) image
region, with the pixels identified through a classification
strategy [181]. These techniques can positively weight pure
pixels that are spatially close to each pixel being unmixed.
This idea was also in other works, such as [182], which performed
SU through a variant of the MESMA algorithm,
and in [183], which used only the spatially closest pure
pixels to process each mixed pixel. Other local unmixing
approaches considered hierarchical segmentation approaches
in which the hyperspectral image was divided
into two spatial scales: a coarse one, where unmixing was
performed with MESMA, and a fine one in which the spectral
libraries were extracted by using the spectral signatures
of small and homogeneous objects [184] or a priori
knowledge about the abundances obtained from external
high-resolution classification maps [185].
An important issue related to local unmixing algorithms
is the determination of the number of EMs contained in each
local image region. While in most experimental works this
was performed empirically and even manually, it is desirable
to have automated methodologies to estimate the number
of local EMs and their spectral signatures. This usually involves
the estimation of the intrinsic dimensionality of the
local subset of the hyperspectral image [186]. However, the
performance of intrinsic dimensionality estimators is often
negatively impacted when the size of the data set is small
[187]. This strongly limits the characteristics (i.e., the size) of
the subsets and the segmentation procedures selected for unsupervised
local unmixing. Collaborative sparse regression
approaches [110] were proposed to deal with the shortcomings
of intrinsic dimensionality estimation by avoiding the
selection of repeated and mixed signatures during unmixing
[188]. The sparsity level was selected via a Bayesian information
criterion to obtain a good compromise between small
REs and a low number of selected signatures.
Divide Image
Into Local Regions
Clustering
Estimated
Abundances and EMs
Observed Image
Unmixing Results
for Local Regions
FIGURE 12. A description of local SU techniques. Local SU addresses the variability of EM signatures across space by performing the process on
small, compact spatial regions of the image in which the EMs can be assumed to be approximately constant. The local SU results for each image
region are then clustered to assemble global abundance maps and sets of EM spectra. Local SU offers a lot of flexibility in the choice of the
segmentation of the image and the local EM extraction and clustering strategies, which can have a significant impact on the global SU results.
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
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IEEE Geoscience and Remote Sensing Magazine - December 2021

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