Joint Gaussian processes for inverse modeling

Solving inverse problems is central in geosciences and remote sensing. Very often a mechanistic physical model of the system exists that solves the forward problem. Inverting the implied radiative transfer model (RTM) equations numerically implies, however, challenging and computationally demanding problems. Statistical models tackle the inverse problem and predict the biophysical parameter of interest from radiance data, exploiting either in situ data or simulated data from an RTM. We introduce a novel nonlinear and nonparametric statistical inversion model which incorporates both real observations and RTM-simulated data. The proposed Joint Gaussian Process (JGP) provides a solid framework for exploiting the regularities between the two types of data, in order to perform inverse modeling. Advantages of the JGP method over competing strategies are shown on both a simple toy example and in leaf area index (LAI) retrieval from Landsat data combined with simulated data generated by the PROSAIL model.