Generalized Herglotz Functions and Inverse Scattering Problem in a Finite Depth Ocean

摘要

In an investigation of underwater acoustic wave inverse scattering problem, namely to recover the shape of a scatterer from the far-field pattern of the scattered wave, it was found that, besides the difficulty that the problem is nonlinear and improperly posed, the most difficult point of the problem comes from the fact that the scattered wave field and the far-field is not 1-1 related. The authors continue the investigation of the problem by seeking an optimal solution in the orthogonal complement of the closure of the set of far field patterns.