Reconstruction algorithms of an inverse conductive scattering problem for the Helmholtz equation

ABSTRACT

In this paper, we consider an inverse conductive scattering problem for the Helmholtz equation from measurements on the outer boundary. We want to seek reconstruction algorithms to detect the number, location, size and shape of inhomogeneities within a body. This problem is nonlinear and ill-posed, thus we should consider regularization techniques in order to improve the corresponding approximation. We examine the viability of our proposed reconstruction algorithms through the use of numerical experiments.

Keywords:

• Inverse conductive scattering problem
• Levenberg–Marquardt algorithm
• trust-region-reflective optimization algorithm
• integral equation
• ill-posed problem

AMS Mathematics Subject Classifications 2010:

• 65N20
• 65N21

Acknowledgments

The research of Ji-Chuan Liu was supported by the Fundamental Research Funds for the Central Universities (No. 2014QNA57) and the NSF of China (No. 11601512, No. 11326236).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of Ji-Chuan Liu was supported by the Fundamental Research Funds for the Central Universities (No. 2014QNA57) and the NSF of China (No. 11601512,11326236).