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Reconstructing planar domains from their moments
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-3125-3030
2000 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 16, no 4, 1053-1070 p.Article in journal (Refereed) Published
Abstract [en]

In many areas of science and engineering it is of interest to find the shape of an object or region from indirect measurements which can actually be distilled into moments of the underlying shapes we seek to reconstruct. In this paper, we describe a theoretical framework for the reconstruction of a class of planar semi-analytic domains from their moments. A part of this class, known as quadrature domains, can approximate, arbitrarily closely, any bounded domain in the complex plane, and is therefore of great practical importance. We provide an exact reconstruction algorithm of quadrature domains. Some numerical demonstrations of the proposed algorithms will be presented. In addition, relations of the present theory to computer-assisted tomography and a geophysical inverse problem will be briefly discussed.

Place, publisher, year, edition, pages
2000. Vol. 16, no 4, 1053-1070 p.
Keyword [en]
2-dimensional l-problem, extremal solutions
URN: urn:nbn:se:kth:diva-20009ISI: 000089064000014OAI: diva2:338702
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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