S. Stephany, F.M. Ramos, H.F. de Campos Velho, C.D. Mobley (1997): Use of an Adaptative Regularization Technique in a Hydrologic Optics Inverse Problem, Proc. of the XX Brazilian Congress on Computing and Applied Mathematics (CNMAC'97), Brazilian Society for Computing and Applied Mathematics (SBMAC), pp. 602-603, Brazil.

Abstract: Most of the implicit inversion methods are based in the minimization of a suitable objective function. Reconstruction of physical parameters from noisy data usually requires the use of a regularization term, which is included in the objective function and weighted by a regularization parameter. An adaptative entropic regularization technique is used in a Hydrologic Optics inverse problem. The parameters to be reconstructed are the absorption and scattering coefficient vertical profiles, respectively a(z) and b(z), where z is the depth. This inverse problem is formulated as a nonlinear constrained optimization problem. A quasi-Newton algorithm of the Fortran NAG Library is used to estimate the parameter vector by solving the minimization problem. The associated direct model is based on the monodimensional (in optical depth) time-independent radiance transfer equation. This equation is numerically solved by the Hydrolight 3.0 code, which uses the invariant imbedding method. The regularization term is based on the maximum entropy principle. Since there is no analytic method for the choice of the regularization parameter, it can be obtained by numerical experimentation ( trial-and-error). Sena and Toksoz proposed an adaptative criterium. Several inversions, using noise corrupted synthetic data, were performed for the estimation of the absorption and scattering vertical profiles using either the trial-and-error or this adaptative criteria and the results are compared.