Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with in situ data that often results in problems with extrapolation outside the study area; and the most widely adopted hybrid modeling by which statistical models, mostly nonlinear and non-parametric machine learning algorithms, are applied to invert RTM simulations. We will focus on the latter. Among the different existing algorithms, in the last decade kernel based methods, and Gaussian Processes (GPs) in particular, have provided useful and informative solutions to such RTM inversion problems. This is in large part due to the confidence intervals they provide, and their predictive accuracy. However, RTMs are very complex, highly nonlinear, and typically hierarchical models, so that very often a single (shallow) GP model cannot capture complex feature relations for inversion. This motivates the use of deeper hierarchical architectures, while still preserving the desirable properties of GPs. This paper introduces the use of deep Gaussian Processes (DGPs) for bio-geo-physical model inversion. Unlike shallow GP models, DGPs account for complicated (modular, hierarchical) processes, provide an efficient solution that scales well to big datasets, and improve prediction accuracy over their single layer counterpart. In the experimental section, we provide empirical evidence of performance for the estimation of surface temperature and dew point temperature from infrared sounding data, as well as for the prediction of chlorophyll content, inorganic suspended matter, and coloured dissolved matter from multispectral data acquired by the Sentinel-3 OLCI sensor. The presented methodology allows for more expressive forms of GPs in big remote sensing model inversion problems.

参数反演和模型反演是遥感和对地观测的关键问题。目前，存在不同的近似方法：直接但成本高昂的辐射传输模型（RTM）反演；使用原位数据进行统计反演，通常会导致研究区域外的外推出现问题；最广泛采用的混合建模，其中统计模型（主要是非线性和非参数机器学习算法）被应用于逆 RTM 模拟。我们将重点关注后者。在不同的现有算法中，在过去的十年中，基于核的方法，特别是高斯过程（GP），已经为此类 RTM 反演问题提供了有用且信息丰富的解决方案。这在很大程度上是由于它们提供的置信区间及其预测准确性。然而，RTM 是非常复杂、高度非线性且典型的分层模型，因此单个（浅层）GP 模型通常无法捕获用于反演的复杂特征关系。这促进了更深层次架构的使用，同时仍然保留了 GP 的理想属性。本文介绍了使用深度高斯过程（DGP）进行生物地球物理模型反演。与浅层 GP 模型不同，DGP 考虑了复杂的（模块化、分层）过程，提供了一种有效的解决方案，可以很好地扩展到大数据集，并提高了单层模型的预测精度。 在实验部分，我们提供了根据红外探测数据估计表面温度和露点温度，以及根据多光谱数据预测叶绿素含量、无机悬浮物和有色溶解物的性能经验证据。 Sentinel-3 OLCI 传感器。所提出的方法允许在大型遥感模型反演问题中采用更具表现力的 GP 形式。