caa a22 4500 475737342 CHVBK 20180406123450.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1007/s001900050288 doi (NATIONALLICENCE)springer-10.1007/s001900050288 Deconvolution with wavelets and vaguelettes [Elektronische Daten] [A. Gilbert, W. Keller] Abstract.: The use of wavelets for the solution of convolution equations is studied as a possible alternative to the well-established Fast Fourier Transform (FFT) technique. Two possible solution strategies are investigated: (1) The use of wavelets for the representation of both the given data and the unknown solution. This leads to an algorithm with good de-noising and data-compression properties. In terms of computational efficiency this algorithm is inferior to FFT. (2) The use of wavelets for the representation of the unknown solution and of so-called vaguelettes for the representations of the given data. This leads to an algorithm which is even faster than FFT. Springer-Verlag Berlin Heidelberg, 2000 Key words: Wavelets - Vaguelette - Galerkin method - Multiscale analysis - Convolution equations - Quadrature formula - Mallat algorithm nationallicence Gilbert A. Geodätisches Institut, Geschwister-Scholl-Strasse 24D, D-70174 Stuttgart, Germany e-mail: wolfgang.keller@gis.uni-stuttgart.de; Tel.: +49 711 121 3459; Fax: +49 711 121 3297, DE aut Keller W. Geodätisches Institut, Geschwister-Scholl-Strasse 24D, D-70174 Stuttgart, Germany e-mail: wolfgang.keller@gis.uni-stuttgart.de; Tel.: +49 711 121 3459; Fax: +49 711 121 3297, DE aut https://doi.org/10.1007/s001900050288 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001900050288 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gilbert A. Geodätisches Institut, Geschwister-Scholl-Strasse 24D, D-70174 Stuttgart, Germany e-mail: wolfgang.keller@gis.uni-stuttgart.de; Tel.: +49 711 121 3459; Fax: +49 711 121 3297, DE aut NATIONALLICENCE 700 1- Keller W. Geodätisches Institut, Geschwister-Scholl-Strasse 24D, D-70174 Stuttgart, Germany e-mail: wolfgang.keller@gis.uni-stuttgart.de; Tel.: +49 711 121 3459; Fax: +49 711 121 3297, DE aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer