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.

翻译：在声学断层学实践中,例如在医学应用和海洋断层学中,声速相对于其背景值的相对偏差通常不超过10-30%。与此同时,在电磁应用中,等效反差可能明显高于60 %。由于反向电磁问题在某种近似于Helmholtz方程式的情况下可以减少,因此可以对不同“声学”对比和相应的“二电”对比的重建结果进行正式比较。在这项工作中,介绍了这种重建的例子,这些重建是通过使用R.G. Novikov作品中描述的功能分析算法取得的。以前,这种算法对于解决声学摄影实际问题的优势得到了证明。目前工作的结果表明,功能分析算法也可以用于重建与高“电量”对比的异异性。此外,功能算法还完美地重建了非常小的“二电”反差,这种反差的恢复可能因疲弱的后退而难以采取其他方法。