Reconstructing planar domains from their moments. (English) Zbl 0959.44010

Gustafsson, Björn; He, Chiyu; Milanfar, Peyman; Putinar, Mihai

Inverse Probl. 16, No. 4, 1053-1070 (2000).

The authors describe a theoretical framework for the reconstruction of a class of planar semi-analytic domains for 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 practical importance.
An exact reconstruction algorithm of quadrature domains and some numerical demonstrations of the proposed algorithms are presented. In addition, relations of the present theory to computer-assisted tomography and a geophysical inverse problem are briefly discussed.

Reviewer: Som Prakash Goyal (Jaipur)

MSC:

44A60	Moment problems
92C55	Biomedical imaging and signal processing
86A22	Inverse problems in geophysics
65R10	Numerical methods for integral transforms

Keywords:

numerical examples; moment problems; planar semi-analytic domains; quadrature domains; reconstruction algorithm; computer-assisted tomography; geophysical inverse problem