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

Gaussian processes (GPs) have experienced tremendous success in biogeophysical parameter retrieval in the last few years. GPs constitute a solid Bayesian framework to consistently formulate many function approximation problems. This article reviews the main theoretical GP developments in the field, considering new algorithms that respect signal and noise characteristics, extract knowledge via automatic relevance kernels to yield feature rankings automatically, and allow applicability of associated uncertainty intervals to transport GP models in space and time that can be used to uncover causal relations between variables and can encode physically meaningful prior knowledge via radiative transfer model (RTM) emulation. The important issue of computational efficiency will also be addressed. These developments are illustrated in the field of geosciences and remote sensing at local and global scales through a set of illustrative 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.

[1]  Mathias Disney,et al.  Efficient Emulation of Radiative Transfer Codes Using Gaussian Processes and Application to Land Surface Parameter Inferences , 2016, Remote. Sens..

[2]  Jan G. P. W. Clevers,et al.  Optical remote sensing and the retrieval of terrestrial vegetation bio-geophysical properties - A review , 2015 .

[3]  Jan G. P. W. Clevers,et al.  Experimental Sentinel-2 LAI estimation using parametric, non-parametric and physical retrieval methods - A comparison , 2015 .

[4]  Andrew Gordon Wilson,et al.  Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP) , 2015, ICML.

[5]  Luis Alonso,et al.  Gaussian processes retrieval of leaf parameters from a multi-species reflectance, absorbance and fluorescence dataset. , 2014, Journal of photochemistry and photobiology. B, Biology.

[6]  Gustavo Camps-Valls,et al.  Retrieval of Biophysical Parameters With Heteroscedastic Gaussian Processes , 2014, IEEE Geoscience and Remote Sensing Letters.

[7]  Wolfgang Lucht,et al.  A high‐resolution approach to estimating ecosystem respiration at continental scales using operational satellite data , 2014, Global change biology.

[8]  M. S. Moran,et al.  Global and time-resolved monitoring of crop photosynthesis with chlorophyll fluorescence , 2014, Proceedings of the National Academy of Sciences.

[9]  Soteris A. Kalogirou,et al.  Chapter 11 – Designing and Modeling Solar Energy Systems , 2014 .

[10]  J. Verrelst,et al.  Mapping a priori defined plant associations using remotely sensed vegetation characteristics , 2014 .

[11]  Gustavo Camps-Valls,et al.  Gaussian processes uncertainty estimates in experimental Sentinel-2 LAI and leaf chlorophyll content retrieval , 2013 .

[12]  Frédéric Baret,et al.  GEOV1: LAI and FAPAR essential climate variables and FCOVER global time series capitalizing over existing products. Part1: Principles of development and production , 2013 .

[13]  B. Harnisch,et al.  On the demands on imaging spectrometry for the monitoring of global vegetation fluorescence from space , 2013, Optics & Photonics - Optical Engineering + Applications.

[14]  José F. Moreno,et al.  Gaussian Process Retrieval of Chlorophyll Content From Imaging Spectroscopy Data , 2013, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[15]  Masashi Sugiyama,et al.  Least-squares independence regression for non-linear causal inference under non-Gaussian noise , 2011, Machine Learning.

[16]  Miguel Lázaro-Gredilla,et al.  Bayesian Warped Gaussian Processes , 2012, NIPS.

[17]  Kamaruzzaman Sopian,et al.  A review of solar energy modeling techniques , 2012 .

[18]  C. Donlon,et al.  The Global Monitoring for Environment and Security (GMES) Sentinel-3 mission , 2012 .

[19]  P. Levelt,et al.  ESA's sentinel missions in support of Earth system science , 2012 .

[20]  Matthias Drusch,et al.  Sentinel-2: ESA's Optical High-Resolution Mission for GMES Operational Services , 2012 .

[21]  Nadine Gobron,et al.  An Earth Observation Land Data Assimilation System (EO-LDAS) , 2012 .

[22]  Luis Alonso,et al.  Retrieval of Vegetation Biophysical Parameters Using Gaussian Process Techniques , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[23]  Luis Alonso,et al.  Machine learning regression algorithms for biophysical parameter retrieval: Opportunities for Sentinel-2 and -3 , 2012 .

[24]  Simon J. Hook,et al.  Synergies Between VSWIR and TIR Data for the Urban Environment: An Evaluation of the Potential for the Hyperspectral Infrared Imager (HyspIRI) , 2012 .

[25]  Filomena Romano,et al.  An Advanced Model for the Estimation of the Surface Solar Irradiance Under All Atmospheric Conditions Using MSG/SEVIRI Data , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[26]  Andrew Gordon Wilson,et al.  Gaussian Process Regression Networks , 2011, ICML.

[27]  Luis Gómez-Chova,et al.  Remote Sensing Image Processing , 2011, Remote Sensing Image Processing.

[28]  A. Arneth,et al.  Global patterns of land-atmosphere fluxes of carbon dioxide, latent heat, and sensible heat derived from eddy covariance, satellite, and meteorological observations , 2011 .

[29]  Miguel Lázaro-Gredilla,et al.  Variational Heteroscedastic Gaussian Process Regression , 2011, ICML.

[30]  J. Nichol,et al.  Improved forest biomass estimates using ALOS AVNIR-2 texture indices , 2011 .

[31]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[32]  Clemens Beckstein,et al.  Characterization of ecosystem responses to climatic controls using artificial neural networks , 2010 .

[33]  F. Woodward,et al.  Terrestrial Gross Carbon Dioxide Uptake: Global Distribution and Covariation with Climate , 2010, Science.

[34]  Olga Sykioti,et al.  Monitoring canopy biophysical and biochemical parameters in ecosystem scale using satellite hyperspectral imagery: An application on a Phlomis fruticosa Mediterranean ecosystem using multiangular CHRIS/PROBA observations , 2010 .

[35]  Carl E. Rasmussen,et al.  Sparse Spectrum Gaussian Process Regression , 2010, J. Mach. Learn. Res..

[36]  Aapo Hyvärinen,et al.  Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity , 2010, J. Mach. Learn. Res..

[37]  Demetrio Labate,et al.  The PRISMA payload optomechanical design, a high performance instrument for a new hyperspectral mission , 2009 .

[38]  W. Verhoef,et al.  PROSPECT+SAIL models: A review of use for vegetation characterization , 2009 .

[39]  Shunlin Liang,et al.  Earth system science related imaging spectroscopy — an assessment , 2009 .

[40]  Bernhard Schölkopf,et al.  Regression by dependence minimization and its application to causal inference in additive noise models , 2009, ICML '09.

[41]  Hans-Georg Beyer,et al.  Irradiance Forecasting for the Power Prediction of Grid-Connected Photovoltaic Systems , 2009, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[42]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[43]  Soteris A. Kalogirou,et al.  Designing and Modeling Solar Energy Systems , 2009 .

[44]  Bernhard Schölkopf,et al.  Nonlinear causal discovery with additive noise models , 2008, NIPS.

[45]  Markus Eck,et al.  Case Studies on the Use of Solar Irradiance Forecast for Optimized Operation Strategies of Solar Thermal Power Plants , 2008, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[46]  Philip Lewis,et al.  Assimilating canopy reflectance data into an ecosystem model with an Ensemble Kalman Filter , 2008 .

[47]  Benjamin Recht,et al.  Random Features for Large-Scale Kernel Machines , 2007, NIPS.

[48]  Wolfram Burgard,et al.  Most likely heteroscedastic Gaussian process regression , 2007, ICML '07.

[49]  Michael E. Schaepman,et al.  A review on reflective remote sensing and data assimilation techniques for enhanced agroecosystem modeling , 2007, Int. J. Appl. Earth Obs. Geoinformation.

[50]  S. Durbha,et al.  Support vector machines regression for retrieval of leaf area index from multiangle imaging spectroradiometer , 2007 .

[51]  Zoubin Ghahramani,et al.  Local and global sparse Gaussian process approximations , 2007, AISTATS.

[52]  F. Baret,et al.  Neural network estimation of LAI, fAPAR, fCover and LAI×Cab, from top of canopy MERIS reflectance data : Principles and validation , 2006 .

[53]  Gustavo Camps-Valls,et al.  Retrieval of oceanic chlorophyll concentration with relevance vector machines , 2006 .

[54]  A-Xing Zhu,et al.  Prediction of Continental-Scale Evapotranspiration by Combining MODIS and AmeriFlux Data Through Support Vector Machine , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[55]  U. Benz,et al.  The EnMAP hyperspectral imager—An advanced optical payload for future applications in Earth observation programmes , 2006 .

[56]  Gustavo Camps-Valls,et al.  Composite kernels for hyperspectral image classification , 2006, IEEE Geoscience and Remote Sensing Letters.

[57]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[58]  Neil D. Lawrence,et al.  Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models , 2005, J. Mach. Learn. Res..

[59]  Carl E. Rasmussen,et al.  Assessing Approximate Inference for Binary Gaussian Process Classification , 2005, J. Mach. Learn. Res..

[60]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[61]  John R. Miller,et al.  Hyperspectral vegetation indices and novel algorithms for predicting green LAI of crop canopies: Modeling and validation in the context of precision agriculture , 2004 .

[62]  Carl E. Rasmussen,et al.  Warped Gaussian Processes , 2003, NIPS.

[63]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[64]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[65]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[66]  Michael E. Tipping.  The Relevance Vector Machine , 1999, NIPS.

[67]  M. Kahru,et al.  Ocean Color Chlorophyll Algorithms for SEAWIFS , 1998 .

[68]  Paul W. Goldberg,et al.  Regression with Input-dependent Noise: A Gaussian Process Treatment , 1997, NIPS.

[69]  Christopher K. I. Williams.  Regression with Gaussian processes , 1997 .

[70]  D. Siméoni,et al.  Infrared atmospheric sounding interferometer , 1997 .

[71]  Carl E. Rasmussen,et al.  In Advances in Neural Information Processing Systems , 2011 .

[72]  J. Peñuelas,et al.  The red edge position and shape as indicators of plant chlorophyll content, biomass and hydric status. , 1994 .

[73]  P. Guttorp,et al.  Nonparametric Estimation of Nonstationary Spatial Covariance Structure , 1992 .

[74]  William L. Smith,et al.  Vertical Resolution and Accuracy of Atmospheric Infrared Sounding Spectrometers. , 1992 .

[75]  Warren J. Wiscombe,et al.  NASA Goddard Space Flight Center, Greenbelt, Maryland , 1990 .

[76]  C. Bohren,et al.  An introduction to atmospheric radiation , 1981 .

[77]  A. O'Hagan,et al.  Curve Fitting and Optimal Design for Prediction , 1978 .