Remote sensing of phytoplankton with neural networks

In this paper, a neural network model, realizing a function assigning an estimate of the phytoplankton content in the ocean to several remote sensing acquisitions, is presented. This inverse problem is first shown to be a family of inverse subproblems, all of the same kind and continuously parameterized by the geometrical parameters defining the viewing geometry, thus allowing a two-steps modelling process. The central point of the method is that reflectances and geometrical parameters are processed in a different way. The first ones are considered as random variables while,the seconds play the role of deterministic parameters. First, a set of local regression phytoplankton concentration estimators, i.e. small size neural networks, is constructed, locality being defined in the geometrical parameters space. Under some non restrictive hypotheses, each of those local models is shown to be optimal. Further, a lower bound on the expected accuracy is given. Secondly, a global model is constructed from a set of local models which in fact amounts to be a neural network, the parameters of which are continuous functions of the geometrical parameters. The model has been tested on a wide simulated data. set of about 7 million points for different geometrical configurations, different atmospheric conditions and several wind speed and direction values. It has shown very good results for a large set of geometrical configurations. Moreover, many much results have been obtained with this model than with global approaches based on multilayer perceptrons and radial basis functions neural networks. The presented methodology is also a promising direction for the elaboration of complex models from a set of simpler ones.