A review of some of the author’s results in the area of inverse scattering is given. The following topics are discussed: 1) Property C and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3) Inverse scattering with ”incomplete“ data, 4) Inverse scattering for inhomogeneous Schrödinger equation, 5) Krein’s inverse scattering method, 6) Invertibility of...

For good image quality using ultrasound inverse scattering, one alternately solves the well-posed forward scattering equation for an estimated total field and the ill-posed inverse scattering equation for the desired object property function. In estimating the total field, error or noise contaminates the coefficients of both matrix and data of the inverse scattering equation. Previous work on i...

Abstract—In this paper, the diagnosis of soft faults in lossy electric transmission lines is studied through the inverse scattering approach. The considered soft faults are modeled as continuous spatial variations of distributed characteristic parameters of transmission lines. The diagnosis of such faults from reflection and transmission coefficients measured at the ends of a line can be formul...

Stability of the solutions to 3D inverse scattering problems with fixed-energy data. Abstract A review of the author's results is given. Inversion formulas and stability results for the solutions to 3D inverse scattering problems with fixed energy data are obtained. Inversion of exact and noisy data is considered. The inverse potential scattering problem with fixed-energy scattering data is dis...

An overview of the author's results is given. Property C stands for completeness of the set of products of solutions to homogeneous linear Sturm-Liouville equations. The inverse problems discussed include the classical ones (inverse scattering on a half-line, on the full line, inverse spectral problem), inverse scattering problems with incomplete data, for example, inverse scattering on the ful...

An overview of the author’s results is given. Property C stands for completeness of the set of products of solutions to homogeneous linear Sturm-Liouville equations. The inverse problems discussed include the classical ones (inverse scattering on a half-line, on the full line, inverse spectral problem), inverse scattering problems with incomplete data, for example, inverse scattering on the ful...