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

This paper discusses bivariate scattered data denoising. The proposed method uses second-generation wavelets constructed with the lifting scheme. Starting from a simple initial transform, we propose predictor operators based on a stabilized bivariate generalization 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 coefficients, and hence stabilizes the final estimator. We use a Bayesian thresholding algorithm to denoise the empirical coefficients, and we show the performance of the resulting estimator through a simulation study.