Joint estimation of water column parameters and seabed reflectance combining Maximum Likelihood and unmixing algorithm
Résumé
Bathymetry and Water column constituent estimation is a challenging task for the study of coastal zones. Although most extensively used methods are based on the pixel wise inversion of semi empirical models, we have recently proposed a Maximum Likelihood (ML) method to retrieve such parameters. One limitation of the method is that the seabed reflectance is supposed to be known and homogeneous in a sample zone. We propose here to go beyond this limitation by jointly estimating the bathymetry, the concentrations of the constituents, and the reflectance spectra in an inhomogeneous seabed zone. To do so we introduce a non stationary Likelihood for the sample zone, and we also exploit a triple non-negative matrix factorization. We propose an Estimation-Unmixing (E-U) recursive algorithm to solve the problem. The water column parameters are estimated within the ML step, while the unmixing step allows to recover the bottom reflectance in each pixel. When tested on real hyperspectral data acquired in the Quiberon peninsula on French West coast, the method leads to consistent estimated maps of bathymetry and seabed reflectance.