@article {IOPORT.06108487,
    author       = {Heinen, Dennis and Plonka, Gerlind},
    title        = {Wavelet shrinkage on paths for denoising of scattered data.},
    year         = {2012},
    journal      = {Results in Mathematics},
    volume       = {62},
    number       = {3-4},
    issn         = {1422-6383},
    pages        = {337-354},
    publisher    = {Birkh\"auser Verlag (Springer), Basel},
    doi          = {10.1007/s00025-012-0285-3},
    abstract     = {Summary: We propose a new algorithm for the denoising of multivariate function values given at scattered points in $\Bbb R^d$. The method is based on the one-dimensional wavelet transform that is applied along suitably chosen path vectors at each transform level. The idea can be seen as a generalization of the relaxed easy path wavelet transform by {\it G. Plonka} [Multiscale Model. Simul. 7, No. 3, 1474--1496 (2009; Zbl 1175.65158)] to the case of multivariate scattered data. The choice of the path vectors is crucial for the success of the algorithm. We propose two adaptive path constructions that take into account the distribution of the scattered points as well as the corresponding function values. Further, we present some theoretical results on the wavelet transform along path vectors in order to indicate that the wavelet shrinkage along path vectors can really remove noise. The numerical results show the efficiency of the proposed denoising method.},
    identifier   = {06108487},
}