Lifting scheme using smoothing kernels on non-equispaced data

This paper puts forward a new multiscale decomposition. This can be applied to nonparametric regression, in particular so as to smooth non-equispaced univariate data. We introduce an original version of the lifting scheme which uses smoothing kernels. This multiscale approach can naturally deal with non-equispaced data. Besides we propose an algorithm based on this approach that gives approximations at different scales. This leads to smooth curves corresponding to several degrees of smoothing. We also show experiments on synthetic data and a real example.