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Theoretical analysis demonstrates that three-dimensional inverse scattering problems reduce to one dimension in only three specific cases, highlighting fundamental limits of wave-splitting methods.
It is well known that three-dimensional inverse scattering problems are much more difficult to solve than one-dimensional problems. For this reason, some authors have considered cases where one may transform three-dimensional problems to one dimension, in essence looking for three-dimensional problems which allow a one-dimensional wave-splitting. The authors show that such a reduction can be carried out only in three specific cases.
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Chamberland et al. (1993) studied this question.
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