Functional-analytical methods for the scalar inverse-scattering problems

Valentin A. Burov; Olga D. Rumiantseva

doi:10.1117/12.131892

3 November 1992 Functional-analytical methods for the scalar inverse-scattering problems

Valentin A. Burov, Olga D. Rumiantseva

Proceedings Volume 1843, Analytical Methods for Optical Tomography; (1992) https://doi.org/10.1117/12.131892
Event: Analytical Methods for Optical Tomography, 1991, Zvenigorod, Russian Federation

Abstract

The reconstruction problem of scattering inhomogeneities basing on functional-analytical methods is discussed in the article. One of the main ways for these methods is the mathematical extension of real wave vectors to 'non physical' domain of complex wave vectors. The real wave vectors characterize wave field in the medium, if attenuation is absent; the complex wave vectors correspond to fictitious radiation and reception of inhomogeneous waves. This way allows the solution of the Helmholtz-type equation to be obtained, which is more general than that in a classical variant. Moreover, the functional-analytical methods are a base to create the reconstruction algorithm for two-dimensional (and, as a perspective, three- dimensional) scatterers. The algorithm deals with mean power scatterers, which spectra are localized in a certain domain of space frequencies. the limitations of the space scatterer spectrum depend on the scatterer power. The algorithm provides essential economy of calculation expenditure during the process of the scatterer reconstruction. At the same time, an attempt to reconstruct both two-dimensional mean power inhomogeneities with wide space spectrum and full power inhomogeneities leads to evident instability of the problem, that is inherent to any method of solving the two-dimensional inverse problems for the monochromatic observation regime.

Citation Download Citation

Valentin A. Burov and Olga D. Rumiantseva "Functional-analytical methods for the scalar inverse-scattering problems", Proc. SPIE 1843, Analytical Methods for Optical Tomography, (3 November 1992); https://doi.org/10.1117/12.131892

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