Data reduction is a basic tool when a huge amount of data is given, and so it is extremely useful in surface approximation. In this paper we consider such a problem in the case of gridded data, and we propose the use of a two-stage approach in order to have a remarkable data reduction and, at the same time, a good approximation of the given data. In the first stage, a significant set of points is ... [Show full abstract] selected through a sampling strategy solving a suitable nonlinear system by means of the iterative Jacobi method. In the second stage, the least-squares approximating surface is computed using a "generalization" of the well known inverse multiquadric basis functions. Numerical results are given to show the performance of the method.