On the use of the principle of maximum entropy in bivariate splines least-squares approximation

We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight distribution is determined by maximizing the associated entropy function. This approach, previously applied successfully to polynomials and spline curves, enhances the robustness of the regression model by automatically detecting and down-weighting anomalous data during the fitting process. To demonstrate the effectiveness of the method, we present applications to two image processing problems and further illustrate its potential through two synthetic examples.