  Solving inverse problems is central to geosciences and remote sensing.
Radiative transfer models (RTMs) represent mathematically the physical laws
which govern the phenomena in remote sensing applications (forward models). The
numerical inversion of the RTM equations is a challenging and computationally
demanding problem, and for this reason, often the application of a nonlinear
statistical regression is preferred. In general, regression models predict the
biophysical parameter of interest from the corresponding received radiance.
However, this approach does not employ the physical information encoded in the
RTMs. An alternative strategy, which attempts to include the physical
knowledge, consists in learning a regression model trained using data simulated
by an RTM code. In this work, we introduce a nonlinear nonparametric regression
model which combines the benefits of the two aforementioned approaches. The
inversion is performed taking into account jointly 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. The
JGP automatically detects the relative quality of the simulated and real data,
and combines them accordingly. This occurs by learning an additional
hyper-parameter w.r.t. a standard GP model, and fitting parameters through
maximizing the pseudo-likelihood of the real observations. The resulting scheme
is both simple and robust, i.e., capable of adapting to different scenarios.
The advantages of the JGP method compared to benchmark strategies are shown
considering RTM-simulated and real observations in different experiments.
Specifically, we consider leaf area index (LAI) retrieval from Landsat data
combined with simulated data generated by the PROSAIL model.
