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

V. Delouille, M.H. Jansen, R. Sachs, von

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Abstract

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.
Original languageEnglish
Place of PublicationLouvain-la-Neuve
PublisherKatholieke Universiteit Leuven
Number of pages32
Publication statusPublished - 2003

Publication series

NameIAP Technical Report
Volume0303

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