A Survey on Gaussian Processes for Earth-Observation Data Analysis: A Comprehensive Investigation

Abstract

A comprehensive investigationGUSTAU CAMPS-VALLS, JOCHEM VERRELST, JORDI MUÑOZ-MARÍ, VALERO LAPARRA, FERNANDO MATEO-JIMÉNEZ, AND JOSÉ GÓMEZ-DAN Advances in Machine Learning for Remote Sensing and Geosciences image licensed by ingram publishing 0274-6638/16©2016IEEE ieee Geoscience and remote sensinG maGazine JUNE 2016illustrative examples. In particular, important problems for land, ocean, and atmosphere monitoring are considered, from accurately estimating oceanic chlorophyll content and pigments to retrieving vegetation properties from multi-and hyperspectral sensors as well as estimating atmospheric parameters (e.g., temperature, moisture, and ozone) from infrared sounders.Unprecedented data Stream for Land, ocean, and atmoSphere monitoring The spatiotemporally explicit, quantitative retrieval methods for Earth's surface and atmosphere characteristics are required in a variety of Earth system applications. Optical Earth-observing satellites that are endowed with high temporal resolution enable the retrieval and, hence, the monitoring of climate and biogeophysical variables [1], [2]. With the forthcoming superspectral Copernicus Sentinel-2 (S2) [3] and Sentinel-3 missions [4], as well as the planned EnMAP [5], HyspIRI [6], PRISMA [7], and the European Space Agency's candidate FLEX [8], an unprecedented data stream for land, ocean, and atmosphere monitoring will soon become available to a diverse user community. This vast data stream requires enhanced processing techniques that are accurate, robust, and fast. Additionally, the statistical models should capture plausible physical relationships and explain the problem at hand. A wide variety of biogeophysical retrieval methods have been developed over the last few decades, but only a few of them have made it into operational processing chains, and many are still in their infancy [9]. Essentially, there are two main approaches to the inverse problem of estimating biophysical parameters from spectra: 1) parametric physically based models and 2) nonparametric statistical models. On one hand, parametric, physically based models are commonly used to model biological processes and climate variables in Earth monitoring. These models rely on established physical relationships and implement complex combinations of scientific hypotheses. Unfortunately, they do not exploit empirical data to constrain simulation outcomes; thus, despite their solid physical foundation, they are becoming more obscure because more complex processes, parameterizations, and priors need to be included. These issues give rise to too-rigid solutions and large-model discrepancies (see [10] and the references therein). Alternatively, nonparametric statistical models are typically only concerned with developing data-driven models, paying little attention to the physical rules governing the system. The field has proven to be successful in many disciplines of science and engineering [11], and, in general, nonlinear and nonparametric model instantiations typically lead to a more flexible and improved perfor...

Emulation of Leaf, Canopy and Atmosphere Radiative Transfer Models for Fast Global Sensitivity Analysis

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“…These methods have been amply described in earlier publications (e.g., [5,38,44,46,49,50]). The interested reader can find more details therein.…”

“…Many opportunities appear here to improve the performance of emulators: one could think of including multiple pieces of information in the regression algorithm with multimodal/multiresolution regression, e.g., by combining RTMs for the same problem, to accommodate spatial or temporal relations in the emulation [44,94], and to implement better dimensionality reduction techniques beyond linear PCA to deal with the multi-output problem [95]. Apart from these improvements in the regression algorithm, we raise here the important issue of assessment of the emulator function, e.g., by looking at the Jacobian and Hessian of the transformation [38,96], Bayesian sensitivity analysis [34,97], as well as developing emulators that may deal with coupled RTMs and transformations of coefficients [50].…”

Exploitation of SAR and Optical Sentinel Data to Detect Rice Crop and Estimate Seasonal Dynamics of Leaf Area Index

“…In particular, we used a Gaussian process regression (GPR) model [29]. GPR has been recently introduced as a powerful regression tool in remote sensing studies [30]. The GPR model exploits the relations between the input (e.g., bands spectra) x = [x 1 , .…”

Estimation of FAPAR over Croplands Using MISR Data and the Earth Observation Land Data Assimilation System (EO-LDAS)

“…The use of advanced RT models in such schemes is therefore potentially computationally costly, further compounded by the fact that the gradient needs to be evaluated either numerically by finite differences [52], or using an adjoint of the RT model, which still takes significant time to evaluate. To overcome these limitations, we propose the use of Gaussian Process (GP) emulators [21,64,65]. An emulator provides a prediction of the RT model output with respect to the input parameters.…”