Fields of non-linear regression models for atmospheric correction of satellite ocean-color imagery

Remote sensing of ocean color from space, a problem that consists of retrieving spectral marine reflectance from spectral top-of-atmosphere reflectance, is considered as a collection of similar inverse problems continuously indexed by the angular variables influencing the observation process. A general solution is proposed in the form of a field of non-linear regression models over the set T of permitted values for the angular variables, i.e., as a map from T to some function space. Each value of the field is a regression model that performs a direct mapping from the top-of-atmosphere reflectance to the marine reflectance. Since the spectral components of the field take values in the same variable vector space, the retrievals in individual spectral bands are not independent, i.e., the solution is not just a juxtaposition of independent models for each spectral band. A scheme based on ridge functions is developed to approximate this solution to an arbitrary accuracy, and is applied to the retrieval of marine reflectance in Case 1 waters, for which optical properties are only governed by biogenic content. The statistical models are evaluated on synthetic data as well as actual data originating from the SeaWiFS instrument, taking into account noise in the data. Theoretical performance is good in terms of accuracy, robustness, and generalization capabilities, suggesting that the function field methodology might improve atmospheric correction in the presence of absorbing aerosols and provide more accurate estimates of marine reflectance in productive waters. When applied to SeaWiFS imagery acquired off California, the function field methodology gives generally higher estimates of marine reflectance than the standard SeaDAS algorithm, but the values are more realistic.