IEEE Geoscience and Remote Sensing Magazine - December 2021 - 206

structures. Looking at the literature, most sources dealing
with density estimation involve few dimensions, treat the
problems marginally, and construct parametric models of
the densities. The Gaussianization methodology 1) scales
to very high dimensions, 2) jointly works with all dimensions
through simple orthogonal transforms plus marginal
operations, and 3) does not assume any parametric form
of the density. Using the standard multivariate Gaussian
as a convenient goal distribution in the transform domain
leverages the change-of-variables formula to compute exact
probability densities. And, by extension, we are able to
compute IT metrics easily.
We showed empirical performance evidence in several
Earth system data analysis problems, using a wide diversity
of data (multispectral, hyperspectral, SAR, and global
products from satellites and Earth system models), and
addressed the key problems of information estimation,
redundancy, and synthesis. Our results confirmed the validity
of the method, for which we anticipate wide use and
adoption. The framework enables us to tackle all applications
involving a PDF estimation, from data classification
to denoising and coding, which were not treated in this article.
The methodology also facilitates computing other interesting
IT measures, such as KL divergence and conditional
independence, which will be a subject of future research.
ACKNOWLEDGMENTS
This research was funded by the European Research
Council (ERC), under the ERC-CoG-2014 project (grant
647423) and the ERC-SyG-2019 USMILE project (grant
855187). J. Emmanuel Johnson thanks the European Space
Agency (ESA) for support via the Early Adopter Call of the
Earth System Data Lab project. Additional support was
provided by Project RTI2018-096765-A-100 (MCIU/AEI/
FEDER, UE). Valero Laparra is supported by the projects
TEC2016-77741-R, DPI2017-89867-C2-2-R, and PID2019109026RB-I00.
Maria Piles thanks the ESA for the longterm
support of this initiative.
AUTHOR INFORMATION
J. Emmanuel Johnson (juan.johnson@uv.es) is with the Image
Processing Laboratory, University of Valencia, Valencia,
46010, Spain.
Valero Laparra (valero.laparra@uv.es) is with the Image
Processing Laboratory, University of Valencia, Valencia,
46010, Spain.
María Piles (maria.piles@uv.es) is with the Image Processing
Laboratory, University of Valencia, Valencia, 46010,
Spain. She is a Senior Member of IEEE.
Gustau Camps-Valls (gustau.camps@uv.es) is with the
Image Processing Laboratory, University of Valencia, Valencia,
46010, Spain. He is a Fellow of IEEE.
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IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2021
IEEE Geoscience and Remote Sensing Magazine - December 2021

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