Deconvolution with wavelets and vaguelettes |
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| Authors: | A. Gilbert W. Keller |
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| Affiliation: | Geod?tisches 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
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| 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. Received: 14 October 1998 / Accepted: 30 November 1999 |
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| Keywords: | : Wavelets – Vaguelette – Galerkin method – Multiscale analysis – Convolution equations – Quadrature formula – Mallat algorithm |
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