IEEE Geoscience and Remote Sensing Magazine - December 2021 - 253

by varying the values of 1
n and n While (20) is approxi2
.
mately linear for small albedo values, important nonlinearities
occur for large albedo values [52].
Additionally, we explore variability introduced by errors
occurring in a simple atmospheric compensation
model, where the reflectance of each pixel at each wavelength
is obtained by dividing the corresponding pixel's
radiance by the radiance observed at a perfectly reflective
calibration panel [271, Sec. 5(a)(1)], [315]. Assuming full
visibility and that the adjacency effect is negligible, this
model is given by
yyEE
EE
sensor = s
sungrsky
sungrsky
-
-
n
n
2
1
+
+
,
(21)
where ys and ysensor denote the reflectance at the ground and
the sensor, Esungrthe
ground level, and Esky
represents the solar radiance observed at
is the skylight. Parameters n 1
and 2n are the cosines of the angles between the surface
normal and the direction of the sun at each pixel and at the
calibration panel, respectively. By fixing ,2
n
1
Esungr,
and Esky
a priori, n can be varied to simulate spectral signatures at
different viewing geometries.
GENERATING THE MIXED PIXELS
Finally, each pixel can be generated according to the spectral
variability-accommodating LMM described in (2), with the
EM for each pixel (Mn
columns) sampled randomly from
the set of synthetically generated signatures. Additive noise
can be introduced to obtain a desired signal-to-noise ratio.
SOFTWARE RESOURCES
Several software packages are available to perform SU with
spectral variability. Classical techniques, such as MESMA and
some of its alternatives (including library pruning and transformation
methods), can be found in the Visualization and
Image Processing for Environmental Research tools software
package [316], which is available as a plug-in for well-established
software, such as ENVI and the Quantum Geographic
Information System. An implementation of the MESMA algorithm
is also available in R in the remote sensing toolbox.
Algorithms that were developed more recently, on the other
hand, are usually available only as stand-alone prototypes
implemented in MATLAB and Python. A list of software packages
for some of the papers reviewed in this work (most of
which are found at the authors' websites) is in Table 3. Also,
TABLE 3. COMPUTATIONAL CODE CONTAINING IMPLEMENTATIONS OF SOME OF THE WORKS REVIEWED IN THIS ARTICLE.
METHOD
LINK
METHODS THAT USE SPECTRAL LIBRARIES
MESMA [37], AAM [87]
SUnSAL [103], SUnSAL-TV [112]
Sparse SU with mixed norms [84]
BAYESIAN METHODS
BCM [255]
NCM-E (NCM by Eches et al.) [239]
UsGNCM [242]
Bayesian OU [254]
PCOMMEND [247]
GMM [256]
PARAMETRIC EM MODELS
ELMM [51]
PLMM [217]
GLMM [212]
DeepGUn [222]
MUA-SV [223]
OU [221]
EM-MODEL-FREE METHODS
RUSAL [227]
SULoRa [229]
ALMM [228]
ULTRA-V [230]
https://sites.google.com/site/robheylenresearch/code/AAM
.zip?attredirects=0&d=1
http://www.lx.it.pt/~bioucas/publications.html
https://openremotesensing.net/knowledgebase/hyperspectral-image-unmixing
-with-endmember-bundles-and-group-sparsity-inducing-mixed-norms/
https://github.com/GatorSense/BetaCompositionalModel
http://olivier.eches.free.fr/research.html
https://sites.google.com/site/abderrahimhalimi/publications
https://pthouvenin.github.io/robust-unmixing-plmm/
https://github.com/GatorSense/PCOMMEND
https://github.com/zhouyuanzxcv/Hyperspectral
https://openremotesensing.net/knowledgebase/spectral-variability-and
-extended-linear-mixing-model/
https://pthouvenin.github.io/unmixing-plmm/
https://github.com/talesimbiriba/GLMM
LANGUAGE
MATLAB
MATLAB
MATLAB
MATLAB
MATLAB
MATLAB
MATLAB
MATLAB
MATLAB
MATLAB
MATLAB
MATLAB
https://github.com/ricardoborsoi/Unmixing_with_Deep_Generative_Models MATLAB
https://github.com/ricardoborsoi/DataDependentSUvarRelease
https://pthouvenin.github.io/online-unmixing-plmm/
MATLAB
MATLAB
https://sites.google.com/site/abderrahimhalimi/publications
https://sites.google.com/view/danfeng-hong/data-code
https://openremotesensing.net/knowledgebase/an-augmented-linear-mixing
-model-to-address-spectral-variability-for-hyperspectral-unmixing/
https://github.com/talesimbiriba/ULTRA-V
MATLAB
MATLAB
MATLAB
MATLAB
The code was provided by its respective authors. AAM: alternating angle minimization; SUnSAL: sparse unmixing via variable splitting and augmented Lagrangian; TV: total variation;
BCM: beta compositional model; NCM-E: NCM published by Eches et al.; UsGNCM: unsupervised generalized NCM; OU: online unmixing; PCOMMEND: piecewise convex multiple-model
EM detection and SU; GMM: Gaussian mixture model; DeepGUn: deep generative unmixing; MUA-SV: multiscale unmixing algorithm accounting for spectral variability; RUSAL: robust
unmixing by variable splitting and augmented Lagrangian; SULoRa: subspace unmixing with low-rank attribute embedding; ALMM: augmented LMM; ULTRA-V: unmixing with low-rank
tensor regularization algorithm.
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
253
https://sites.google.com/site/robheylenresearch/code/AAM.zip?attredirects=0&d=1 https://sites.google.com/site/robheylenresearch/code/AAM.zip?attredirects=0&d=1 http://www.lx.it.pt/~bioucas/publications.html https://openremotesensing.net/knowledgebase/hyperspectral-image-unmixing-with-endmember-bundles-and-group-sparsity-inducing-mixed-norms/ https://openremotesensing.net/knowledgebase/hyperspectral-image-unmixing-with-endmember-bundles-and-group-sparsity-inducing-mixed-norms/ https://www.github.com/GatorSense/BetaCompositionalModel http://olivier.eches.free.fr/research.html https://sites.google.com/site/abderrahimhalimi/publications https://pthouvenin.github.io/robust-unmixing-plmm/ https://www.github.com/GatorSense/PCOMMEND https://www.github.com/zhouyuanzxcv/Hyperspectral https://openremotesensing.net/knowledgebase/spectral-variability-and-extended-linear-mixing-model/ https://openremotesensing.net/knowledgebase/spectral-variability-and-extended-linear-mixing-model/ https://pthouvenin.github.io/unmixing-plmm/ https://www.github.com/talesimbiriba/GLMM https://www.github.com/ricardoborsoi/Unmixing_with_Deep_Generative_Models https://www.github.com/ricardoborsoi/DataDependentSUvarRelease https://pthouvenin.github.io/online-unmixing-plmm/ https://sites.google.com/site/abderrahimhalimi/publications https://sites.google.com/view/danfeng-hong/data-code https://openremotesensing.net/knowledgebase/an-augmented-linear-mixing-model-to-address-spectral-variability-for-hyperspectral-unmixing/ https://openremotesensing.net/knowledgebase/an-augmented-linear-mixing-model-to-address-spectral-variability-for-hyperspectral-unmixing/ https://www.github.com/talesimbiriba/ULTRA-V

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