ON THE RECONSTRUCTION OF LOW-FREQUENCY MOMENTS IN ACOUSTIC SCATTERING

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.