Retrieval of Biophysical Parameters With Heteroscedastic Gaussian Processes

An accurate estimation of biophysical variables is the key to monitor our Planet. Leaf chlorophyll content helps in interpreting the chlorophyll fluorescence signal from space, whereas oceanic chlorophyll concentration allows us to quantify the healthiness of the oceans. Recently, the family of Bayesian nonparametric methods has provided excellent results in these situations. A particularly useful method in this framework is the Gaussian process regression (GPR). However, standard GPR assumes that the variance of the noise process is independent of the signal, which does not hold in most of the problems. In this letter, we propose a nonstandard variational approximation that allows accurate inference in signal-dependent noise scenarios. We show that the so-called variational heteroscedastic GPR (VHGPR) is an excellent alternative to standard GPR in two relevant Earth observation examples, namely, Chl vegetation retrieval from hyperspectral images and oceanic Chl concentration estimation from in situ measured reflectances. The proposed VHGPR outperforms the tested empirical approaches, as well as statistical linear regression (both least squares and least absolute shrinkage and selection operator), neural nets, and kernel ridge regression, and the homoscedastic GPR, in terms of accuracy and bias, and proves more robust when a low number of examples is available.