On the reconstruction of low-frequency moments in acoustic scattering

Charalambopoulos, A.

doi:10.1090/S0033-569X-2012-01264-X

Author: A. Charalambopoulos
Journal: Quart. Appl. Math. 70 (2012), 311-343
MSC (2010): Primary 35R30, 76Q05; Secondary 35J05
DOI: https://doi.org/10.1090/S0033-569X-2012-01264-X
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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