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Inverse scattering solutions of scalar Helmholtz wave equation by a multiple source moment method

Inverse scattering solutions of scalar Helmholtz wave equation by a multiple source moment method

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© The Institution of Electrical Engineers
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Determining the spatial scattering function, i.e. solving the inverse scattering problem, with the Helmholtz wave equation model is known to be an ill posed problem for a single incident radiation field. We show that the problem becomes well posed if formulated as seeking the common scattering function which produces a best prediction of the given scattering data for sufficiently many sources and receivers. The scattering function is found by solution of a system of non-linear algebraic equations which are derived by the method of moments. Our method avoids perturbation theory approximations.

Inspec keywords: wave equations; picture processing; nonlinear equations; electromagnetic wave scattering; modelling

Other keywords: receivers; nonlinear algebraic equations; scattering data; spatial scattering function; image reconstruction; EM wave scattering; inverse scattering; picture processing; model; single incident radiation field; common scattering function; scalar Helmholtz wave equation; multiple source moment method; sources

Subjects: Optical information, image and video signal processing; Nonlinear and functional equations (numerical analysis)

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