Surface reconstruction from ship track data using a recursive method

The problem of constructing a smooth surface from large datasets coming from different measurements (teledetection, topography, ship track data...) appears in many instances in oceanography, geophysics and geology. One can think for instance of the problem of reconstructing seafloor surfaces from SONAR ship track bathymetry data. Another example is the construction of a Digital Elevation Model from a given set of topography isolines,. Classical algorithms used to solve this class of problems usually select points on the curves to define a Lagrange dataset, and subsequently make use of classical spline functions, bivariate splines, or spline functions in Hilbert spaces. In this work, we propose an approximation method that honors the continuous aspect of the data. We use a fidelity criterion to the data, of integral type, which is based upon a L2-norm. In this respect, the method is related to the surface approximation technique introduced in the context of partial datasets by Gout et al.