On the reconstruction of low-frequency moments in acoustic scattering

Author:
A. Charalambopoulos

Journal:
Quart. Appl. Math. **70** (2012), 311-343

MSC (2010):
Primary 35R30, 76Q05; Secondary 35J05

Published electronically:
February 29, 2012

MathSciNet review:
2953106

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Abstract: The inverse scattering method via low-frequency moments was introduced several years ago. The specific structure of moments permitted the construction of a linear inversion algorithm that was based on the assumption that the moments were known, at least theoretically. The present work goes deeper and aims at providing a systematic method to reconstruct these moments from measurements. This turns out to be a demanding inverse problem by itself, serving to establish a realistic implementation for the underlying inversion method. It is proved herein how to determine a specific large class of moments. In addition it is proved that not all the moments are able to be determined purely from the set of data. A demanding integral equation methodology is produced to estimate the large class of the remaining moments that are not directly accessible from measurements.

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Additional Information

**A. Charalambopoulos**

Affiliation:
Department of Materials Science and Engineering, The University of Ioannina, 45110 Greece

DOI:
https://doi.org/10.1090/S0033-569X-2012-01264-X

Received by editor(s):
September 23, 2010

Published electronically:
February 29, 2012

Article copyright:
© Copyright 2012
Brown University