An Injective Far-Field Pattern Operator And Inverse Scattering Problem In A Finite Depth Ocean
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An Injective Far-Field Pattern Operator And Inverse Scattering Problem In A Finite Depth Ocean

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    The inverse scattering problem for acoustic waves, which consists of recovering the shape of a scatterer from the far-field pattern of the scattered field, forms the basis of a wide variety of areas in the engineering sciences; however, nearly all intensive efforts in this field are devoted to the cases of R2 and R3. In the case of homogeneous finite depth ocean, the `propagating' far-field pattern can only carry the information from the N+1 propagating modes; this loss of information makes this problem different from that in the whole space case in that the far-field pattern operator is not injective. A formulation of the corresponding direct problem, i.e., of the exterior boundary value problem for the time harmonic acoustic scattering by a soft object, is presented, followed by some properties of the far-field pattern operator. This information is used to construct an injective far-field pattern operator in a suitable subspace. Based on this construction an optimal scheme for solving the inverse scattering problem is presented using the minimizing Tikhonov functional.
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