Geodesic
Inverse problem for acoustical scattering in space with local inhomogeneity
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 16, Tome 156 (1986), pp. 24-34

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Homogeneous space contains a compact inclusion where the wave velocity is variable. It is irradiated by plane waves propagating in various directions. The inverse problem is to reconstruct the velocity from the scattering amplitude determined as asymptotics of scattered waves in infinity. A procedure of reconstruction and the uniqueness theorem are described in the article. 
@article{ZNSL_1986_156_a2,
     author = {M. I. Belishev and Ya. V. Kurylev},
     title = {Inverse problem for acoustical scattering in space with local inhomogeneity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {24--34},
     publisher = {mathdoc},
     volume = {156},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a2/}
}
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M. I. Belishev; Ya. V. Kurylev. Inverse problem for acoustical scattering in space with local inhomogeneity. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 16, Tome 156 (1986), pp. 24-34. http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a2/