Numerical differentiation of 2D functions from noisy data

In this paper, we present a method for the numerical differentiation of bivariate functions when a set of noisy data is given. We suppose we have a sample coming from an independent process with unknown covariance matrix. We construct the gradient estimator using a multiresolution analysis and the usual difference operators. The asymptotic properties of the estimator are studied and convergence results are provided. The method is suitable for any data configuration.