Orthogonality sampling type methods for an inverse acoustic scattering problem
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We consider the inverse acoustic scattering problem of determining the location and shape of penetrable scattering objects from multi-static Cauchy data of the scattered field. We propose two novel imaging functionals of orthogonality sampling type for solving the inverse problem. These imaging functionals, like the orthogonality sampling method, are fast, simple to implement, and robust with respect to noise in the data. A further advantage is that they are applicable to both near-field and far-field data. In particular, in the case of far-field data, the functionals can be easily modified such that only the scattered field data is needed. The theoretical analysis of the first imaging functional relies on the Factorization method along with the Funk-Hecke formula and a relation between the Cauchy data and the scattering amplitude of the scattered field. The second one is justified using the Helmholtz integral representation for the imaginary part of the Green's function of the direct scattering problem. Numerical examples are presented to illustrate the efficiency of the proposed imaging functionals.
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