Inverse scattering problem

In physics, in the area of scattering theory, the inverse scattering problem is the problem of determining the characteristics of an object (its shape, internal constitution, etc.) from measurement data of radiation or particles scattered from the object.

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In mathematics, inverse scattering refers to the determination of the solutions of a set of differential equations based on known asymptotic solutions, that is, on solving the S-matrix. Examples of equations that have been solved by inverse scattering are the Schroedinger equation, the KdV equation and the KP equation.

It is the inverse problem to the direct scattering problem, which is determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer.

Since its early statement for radiolocation, the problem has found vast number of applications, such as echolocation, geophysical survey, nondestructive testing, medical imaging, quantum field theory, to name just a few.

See also: Inverse scattering transform