IEEE Geoscience and Remote Sensing Magazine - December 2021 - 198

are very similar to the real data in Figure 5(b) across all pairwise
band combinations. It is important to note that some of
the most widely used methods, such as PCA, could replicate
Figure 5(a) with a good approximate mean and standard deviation,
but they would not be able to duplicate Figure 5(d),
where all joint distributions are approximately Gaussian.
INFORMATION IN HIGH-RESOLUTION IMAGES
Very-high-resolution images are constantly acquired by
the new generation of sensors on airborne and spaceborne
platforms. A systematic analysis of the images is necessary.
Machine learning and, in particular, deep learning have
led to an important leap in classification accuracy. However,
owing to the wealth of data and their diversity, it becomes
necessary to design algorithms that exploit most of
the images' information content in terms of relevant features
and examples. We validate RBIG to estimate the total
correlation (multi-information) in a set of aerial scenes
collected in the University of California, Merced, data set
[53], which contains manually extracted images from the
United States Geological Survey's National Map Urban
Area Imagery collection, from 21 aerial scene categories,
I1
I2
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250
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(a)
050 100 150 200 250
3
2
1
-1
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(b)
-2
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1
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(c)
FIGURE 4. Radar image processing. We illustrate the Gaussianization of 2D radar data comprised of a pair (I1, I2) of ERS-2 SAR backscattering
intensities. (a) The joint distribution is non-Gaussian, and preprocessing before applying any algorithm is generally convenient. The (b)
standard marginal Gaussianization does not achieve a full spherical (joint) Gaussian, unlike (c) the RBIG transformation [75], [76].
9,000
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Real
Generated
0255075 100 125
Wavelength, λ (nm)
(a)
150 175 200
10 20 50 100 150
(b)
10 20 50 100 150
(c)
FIGURE 5. The Gaussianization and synthesis of hyperspectral data, using RBIG. In (a) we show the mean and standard deviation spectrum
for the 21,000 real pixels (mean = black; standard deviation = darker shade) and the 1 million pixels generated synthetically (mean = red;
standard deviation = lighter shade) using RBIG. In (b) and (c), we show the marginal and joint distributions of 10, 20, 50, 100, and 150 spectral
bands for the real data and for data generated with RBIG, respectively. Plots were generated with corner [77].
198
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2021
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IEEE Geoscience and Remote Sensing Magazine - December 2021

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - December 2021

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