IEEE Geoscience and Remote Sensing Magazine - December 2021 - 197

compare to the popular Pearson correlation coefficient for different
toy data sets.
ILLUSTRATIVE EXPERIMENTS
In this section, we explore the information content, redundancy,
and relation in a selection of Earth data analysis problems
involving remote sensing data and models, using RBIG.
First, we illustrate the method's ability to analyze standard
remote sensing settings involving total correlation estimation
in hyperspectral, radar, and very-high-resolution imagery.
Second, we quantify the information content of several
variables that describe a soil-vegetation status and investigate
the temporal scales leading to the maximum shared
information for the detection and precursors of anomalies,
such as droughts. Finally, we explore the challenging problems
of IT measurement estimates and the quantification
of the spatiotemporal information tradeoff in global Earth
products. Table 3 summarizes the experiments in terms of
measures, applications, and data/simulations.
GAUSSIANIZATION IN REMOTE SENSING DATA
This first set of experiments considers the use of RBIG for
standard remote sensing image processing. We show the
performance of RBIG in hyperspectral, very-high-resolution,
and radar imagery and for several applications: joint
(multivariate) Gaussianization, data synthesis, and information
estimation.
GAUSSIANIZATION OF RADAR IMAGES
The first part of the experiment focuses on the analysis of
radar imagery. The data were collected in the Urban Expansion
Monitoring (UrbEx) project, a part of the European
Space Agency's European Space Research Institute
Data User Program [51]. Results from the UrbEx project
were used to perform the analysis of the selected test
sites and for validation purposes. We consider a European
Remote Sensing Satellite 2 (ERS-2) SAR pair selected with
perpendicular baselines between 20 and 150 m to obtain
the interferometric coherence. The corresponding pair
(, )II
12 of SAR backscattering intensities (0-35 days) was
stacked for analysis; see Figure 4. The relation between the
intensity features is strongly nonlinear and non-Gaussian
and shows a large dispersion; see Figure 4(a). The total correlation,
T, computed with RBIG for the original domain is
T ..0 0929b
=
A standard approach in SAR image (pre)processing
consists of noise removal and marginal Gaussianization,
which can address these problems only partially.
This marginal Gaussianization cannot deal with the saturation
for high and low signal values [Figure 4(b)]. A multivariate
Gaussianization leads to a fully Gaussian density
[Figure 4(c)]. This is confirmed by the estimated total correlation
of
=
Gaussianized data.
SYNTHESIZING HYPERSPECTRAL IMAGES
To show the ability of the method to deal with high-dimensional
data, we consider hyperspectral image processing.
We took the standard Airborne Visible/Infrared Imaging
Spectrometer Indian Pines data set [52], where the data
have spectral redundancy and complex joint distributions.
The images contain 200 spectral channels, constituting the
(very high) input dimensionality. We learned a Gaussianization
transform that led to a multivariate Gaussian domain
of 200-dimension spectral bands. Then, we selected from a
multivariate Gaussian n 106
=
samples of 200 dimensions
and inverted them back to the spectral domain. RBIG can be
used this way to easily generate synthetic spectra. Figure 5(a)
presents the original and synthesized spectra. It shows
how the proposed method enables us to generate/synthesize
seemingly spectral distributions, even in such a highdimensional
setting. Figure 5(b) and (c) gives corner plots
illustrating joint distributions among various spectral bands
(10, 20, 50, 100, and 150). We see that the marginal and joint
distributions for the RBIG-generated spectra in Figure 5(c)
TABLE 3. A SUMMARY OF EXPERIMENTS, WITH DETAILS OF THE DATA SETS, CONFIGURATIONS, APPLICATIONS,
AND MEASURES EMPLOYED.
EXPERIMENT DATA SET
SAR: European Remote Sensing
Satellite 2
1
Hyperspectral: Airborne Visible/Infrared
Imaging Spectrometer
Airborne camera: red-green-blue
images
2
Optical: Moderate Resolution Imaging
Spectroradiometer land surface
temperature, normalized-difference
vegetation index
Passive microwave: Soil Moisture and
Ocean Salinity (SMOS) soil moisture,
vegetation optical depth
3
Observed and simulated: evaporation,
SH, precipitation
CHARACTERISTICS REFERENCE CONFIGURATION APPLICATION MEASURES
Pixel-wise
26 m, backscatter
intensity
10 cm, 21 classes,
100 images/class
0.05º, 5.5 years,
14 days
25 km, 5.5 years,
daily
0.083º, 10 years,
monthly, global
[51]
30 m, 224 channels [52]
[53]
[54]
Pixel-wise
Spatial
Temporal
Gaussianization T
Synthesis
I quantification
I quantification,
PDF comparison
[55]
[56]
Temporal
Spatiotemporal
I quantification,
PDF comparison
I quantification
T
T
H, MI
T .,0 0095b as it is less than the marginally
H, MI
I, H
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
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IEEE Geoscience and Remote Sensing Magazine - December 2021

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