The linear sampling method for sparse small aperture data

Abstract

In an effort to improve the performance of the linear sampling method in situations involving sparse data-sets, this method in inverse scattering has recently been extended from the frequency domain to the time domain. In this paper, we consider the relative merits of the time and multifrequency linear sampling methods for sparse, limited aperture, and data-sets. Among our conclusions are that, for limited aperture measurements single-frequency data can fail to reconstruct the scatterer, whereas both time and multifrequency domain data perform satisfactorily. On the other hand, if the aperture is too small all the sampling methods fail and increasing the number of measurements in a fixed size aperture is of no help.

Keywords:

• linear sampling
• inverse scattering
• multifrequency
• time domain

AMS Subject Classifications:

• 34L25
• 65L09

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of YG was supported by a grant from the National Natural Science Foundation of China [grant number 91230119], [grant number 41474102]; and work of DLC and PM was supported in part by AFOSR [grant number FA 9550-13-1-0199].