Remarks on the Born approximation and the Factorization Method

Abstract

In this paper, we compare the far-field operators for the full nonlinear inverse scattering problem with the Born approximation as its linearization. The Factorization Method shows that both operators share the same behavior with respect to illposedness of the inverse problem. The results are derived for acoustic and electromagnetic scattering problems and the corresponding problem in electrical impedance tomography.

Keywords:

• Born approximation
• Inverse scattering problem
• Factorization Method

AMS Subject Classifications:

• 35P25
• 35J05

Notes

No potential conflict of interest was reported by the authors.

1 Therefore, it would be no restriction to take a (bounded) ball for D.

2 even from into .

3 that is, v satisfies the radiation condition (4.7(4.7) ).

Additional information

Funding

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through [CRC 1173].