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Regularization wavelets and multiresolution

Content Provider	Scilit
Author	Freeden, Willi Schneider, Frank
Copyright Year	1998
Description	Journal: Inverse Problems Many problems arising in (geo)physics and technology can be formulated as compact operator equations of the first kind A F = G. Due to the ill-posedness of the equation, a variety of regularization methods are being considered for an approximate solution, where particular emphasis must be put on balancing the data and the approximation error. In doing so one is interested in optimal parameter choice strategies. In this paper our interest lies in an efficient algorithmic realization of a special class of regularization methods. More precisely, we implement regularization methods based on filtered singular-value decomposition as a wavelet analysis. This enables us to perform, for example, Tikhonov-Philips regularization as multiresolution. In other words, we are able to pass over from one regularized solution to another by adding or subtracting so-called detail information in terms of wavelets. It is shown that regularization wavelets as proposed here are efficiently applicable to a future problem in satellite geodesy, viz satellite gravity gradiometry.
Related Links	http://iopscience.iop.org/article/10.1088/0266-5611/14/2/002/pdf
Ending Page	243
Page Count	19
Starting Page	225
ISSN	02665611
e-ISSN	13616420
DOI	10.1088/0266-5611/14/2/002
Journal	Inverse Problems
Issue Number	2
Volume Number	14
Language	English
Publisher	IOP Publishing
Publisher Date	1998-04-01
Access Restriction	Open
Subject Keyword	Journal: Inverse Problems Applied Mathematics Regularization Methods Regularization Wavelets
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Signal Processing Mathematical Physics Computer Science Applications

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