Second generation wavelet methods for denoising of irregularly spaced data in two dimensions

We treat bivariate nonparametric regression, where the design of experiment can be arbitrarily irregular. Our method uses second-generation wavelets built with the lifting scheme: Starting from a simple initial transform, we propose to use some predictor operators based on a generalization in two dimensions of the Lagrange interpolating polynomial. These predictors are meant to provide a smooth reconstruction. Next, we include an update step which helps to reduce the correlation amongst the detail coecients, and hence stabilizes the nal estimator. We use a Bayesian thresholding algorithm to denoise the empirical coecients, and we show the performance of the resulting estimator through a simulation study.