IEEE Geoscience and Remote Sensing Magazine - June 2021 - 69

unmixing (FCLSU) algorithm. Due to the hard ASC, the
abundances cannot be fully represented in a simplex. For this
reason, a partial constraint least-squares unmixing (PCLSU)
[117] model emerges as required without ASC. Bioucas-Dias
et al. [118] relaxed the strong
, norm to the solvable -1
0 -
,
norm in the sparse HU model and designed a fast and generic
optimization algorithm based on the ADMM framework
[14], called sparse unmixing by variable splitting and augmented
Lagrangian (SUnSAL). In [119], a TV spatial regularization is
considered to further enhance the unmixing performance.
Iordache et al. [120] extended the sparse regression model to
the collaborative version regularized by
, norm for SU.
21,
-
Fu et al. [121] proposed a semiblind HU model by correcting
mismatches among the estimated endmembers and pure
spectral signatures from the library. Huang et al. [122] jointly
imposed sparsity and low-rank properties on the abundances
for better estimating abundance maps. Hong et al. [123] devised
an interesting and effective subspace-based abundance
estimation model. The model neatly sidesteps to directly
decompose the HS data in the complex, high-dimensional
space instead of projecting the HS data into a more robust
subspace where the SV tends to be removed in a more generalized
way with low-rank attribute embedding. Beyond the
current framework, Hong et al. [124] further augmented the
basic LMM by fully modeling SVs, e.g., principal scaling factors
and other SVs that should be incoherent or low coherent
with endmembers, to yield an interpretable and more intelligent
SU model, called augmented LMM (ALMM).
The nonconvexity of these methods on priors, constraints,
or modeling can be summarized as
◗ FCLSU [116]: AA,01
$
<
=1
◗ PCLSU [117]: A0$
◗ SUnSAL [118]: AA AA() ,,01
◗ SUnSAL-TV [119]: AA AA$,T 0
()
X ==<
X =+ V
11,
()
R =1
n
n 2
$0
XR x=+ U =- 0
() () ,, ()0
/
N
n=1
n
2
2
p 2
$
W =- + AAX()=
()
2
F
U
*,
:
$
11
,
◗ Collaborative sparse representation [120]: AaX ==
N aA,
21,
◗ Dictionary-adjusted nonconvex sparsity-encouraging regression
[121]: Aa AE EE
2
F
◗ Subspace unmixing with low-rank attribute embedding
(SULoRA) [123]: UY UY
A ,0$ where U denotes the subspace projection and
◗ ALMM [124]: AA AJ JVUC$
<
() ,, ()
11,
=+ -
FF where V and J denote the SV
<
AV VV I ,
22
dictionary and corresponding coefficients, respectively.
EXPERIMENTAL STUDY
Real urban HS data acquired by the Hyperspectral Digital
Imagery Collection Experiment (HYDICE) over an urban
area of Texas, United States, in 2015 (the latest version
[185]) are used to evaluate the performance of several selected
SOTA unmixing methods qualitatively,
12/ -
== W =,( )
2
F
11, ,
*
is the nuclear norm that approximates the rank property
of the matrix :
1
of 307 × 307 pixels and 162 spectral bands after removing
noisy bands in the wavelength range of 0.4-2.5 μm at a 2-m
GSD. Moreover, the four main materials (or endmembers)
are investigated in the studied scene, i.e., the asphalt, grass,
trees, and roof. Furthermore, the HySime [93] and VCA
[113] algorithms are adopted to determine the number of
endmembers and extract endmembers from the HS image
(as the initialization for blind SU methods) for all of the
compared algorithms, respectively.
Figure 9 shows the visual comparison between different
SOTA unmixing algorithms in terms of abundance maps.
Because of the consideration of real endmembers extracted
from the HS scene, the last four endmember-guided
SU methods perform evidently better than the blind SU
ones. ELMM models the scaling factors, tending to better
capture the distributions of different materials. The
embedding of nonlocal spatial information enables the
NLHTV method to obtain a more similar shape of abundance
maps to that of the ground truth, yielding comparable
unmixing performance to ELMM. Remarkably, the
unmixing results with regard to the abundance maps of
the SULoRA and ALMM algorithms are superior to those
of other methods because the SVs can be fully considered
by robustly embedding the low-rank attributes in a latent
subspace using SULoRA and characterizing complex, real
scenes more finely using ALMM.
REMAINING CHALLENGES
SU has long been a challenging and widely considered topic
in HS RS. Over the past decades, many SU works have been
proposed in attempts to unmix these mixed spectral pixels
more effectively. Yet some key and essential issues and challenges
still remain unsolved.
◗ Benchmark data: Unlike classification, recognition, and
detection tasks, the ground truth of material abundances
is able to be hardly collected due to the immeasurability
of abundance values in reality. On the other
hand, the spectral signatures (i.e., endmembers) of pure
materials are often acquired in the lab. This usually
leads to uncertain mismatches between real endmembers
and lab ones. It turns out to be urgent to establish
benchmark data sets for SU by drawing support from
more advanced imaging techniques or developing interpretable
ground-truth generation models and processing
chains.
including
, NMF [97], PLMM [99], [186], ELMM [100], [187], NLHTV
[102], FCLSU [116], SUnSAL [118], [188], SULoRA
[123], [189], and ALMM [124], [190]. The HS image consists
JUNE 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
◗ Evaluation criteria: Reconstruction errors (REs) or spectral
angle mappers (SAMs) are the two most commonly
used evaluation indices in SU. It should be noted, however,
that the results of REs or SAMs are not equivalent
to those of unmixing. Related to the issue of benchmark
data, the measurements between real results and
estimated ones are the optimal choice if we have the
ground truth for abundances and endmembers. If not,
developing meaningful and reasonable evaluation indices
(e.g., classification accuracy) should be the top
priority in future work.
69
IEEE Geoscience and Remote Sensing Magazine - June 2021

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