Functional-analytical reconstruction of high contrast inhomogeneities

TL;DR

This paper demonstrates that the functional-analytical algorithm, previously used for acoustic tomography, can effectively reconstruct high-contrast electromagnetic inhomogeneities, including very small contrasts, in inverse Helmholtz problems.

Contribution

It extends the application of the functional-analytical algorithm to high dielectric contrasts in electromagnetic inverse problems, showing its effectiveness beyond acoustic cases.

Findings

Successfully reconstructs high dielectric contrast inhomogeneities.

Effectively recovers very small dielectric contrasts.

Demonstrates the algorithm's versatility across different contrast levels.

Abstract

In practice of acoustic tomography, for example, in medical applications and ocean tomography, the relative deviation of sound speed from its background value usually does not exceed 10-30%. At the same time, in electromagnetic applications, the equivalent contrasts can be noticeably higher than 60%. Since the inverse electromagnetic problem can be reduced in some approximation to Helmholtz equation, a formal comparison of reconstruction results obtained for different "acoustic" contrast and corresponding "dielectric" contrast is possible. In this work examples of such reconstructions are presented, which were obtained by using the functional-analytical algorithm described in works of R.G. Novikov. Previously, the advantages of this algorithm for solving practical problems of acoustic tomography were demonstrated. Results obtained in the present work show that functional-analytical algorithm can also be applied to reconstructing inhomogeneities with high "dielectric" contrast. Moreover, the functional algorithm also perfectly reconstructs very small "dielectric" contrast, recovering of which can be difficult for other approaches due to weak backscattering.