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Abstract We analyze the convergence and approximation error of the inverse Born series, obtaining results that hold under qualitatively weaker conditions than previously known. Our approach makes use of tools from geometric function theory in Banach spaces. An application to the inverse scattering problem with diffuse waves is described.
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On the recovery of two function-valued coefficients in the Helmholtz equation for inverse scattering problems via inverse Born series *
Abstract In this work, we construct the Born and inverse Born approximation and series to recover two function-valued coefficients in the Helmholtz equation for inverse scattering problems from the scattering data at two different wave-numbers. An analysis of the convergence and approximation error of the proposed regularized inverse Born series is provided. The results show that the proposed series converges when the inverse Born approximations of the perturbations are sufficiently small. The preliminary numerical results show the capability of the proposed regularized inverse Born approximation and series for recovering the isotropic inhomogeneous media.
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- Award ID(s):
- 2406313
- PAR ID:
- 10610028
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Inverse Problems
- Volume:
- 41
- Issue:
- 7
- ISSN:
- 0266-5611
- Format(s):
- Medium: X Size: Article No. 075004
- Size(s):
- Article No. 075004
- Sponsoring Org:
- National Science Foundation
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