Generalized wavelets design using Kernel methods. Application to signal processing

Multiresolution representations of data are powerful tools in signal processing. In Harten’s framework, multiresolution transforms are defined by predicting finer resolution levels of information from coarser ones using an operator, called the prediction operator, and defining details (or wavelet coefficients) that are the difference between the exact values and the predicted values. In this paper we present a multiresolution scheme using local polynomial regression theory in order to design a more accurate prediction operator. The stability of the scheme is proved and the order of the method is calculated. Finally, some results are presented comparing our method with the classical methods.