Estimation of vegetation chlorophyll content with Variational Heteroscedastic Gaussian Processes

Abstract

Accurate estimation of biophysical variables is the key to monitor our Planet. In particular, leaf chlorophyll content helps in interpreting the chlorophyll fluorescence signal from space, which is an accurate indicator of the actual state of the vegetation beyond greenness. Recently, the family of Bayesian nonparametric methods has provided excellent results in these situations. A particularly useful method in this framework is the Gaussian Processes regression (GP). However, standard GP assumes that the variance of the noise process is independent of the signal, which does not hold in most of the problems. In this paper, we propose a non-standard variational approximation that allows accurate inference in signal-dependent noise scenarios. We show that the so-called Variational Heteroscedastic Gaussian Process (VHGP) regression is an excellent alternative to standard GP for the retrieval of vegetation chlorophyll content from hyperspectral images. In general VHGP outperforms GP (and many other empirical and machine learning techniques) in accuracy and bias, and reveals more robust when a low number of examples is available.