| Abstract: |
| This talk addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is
represented as a centered complex-valued generalized microlocally isotropic Gaussian random field,
where its covariance and relation operators are characterized as conventional pseudo-differential operators. Regarding the direct scattering problem, the well-posedness is established in the distribution
sense for sufficiently large wavenumbers through analysis of the corresponding Lippmann-Schwinger
integral equation. Furthermore, in the context of the inverse scattering problem, the uniqueness is
attained in recovering the microlocal strengths of both the covariance and relation operators of the
random potential. Notably, this is accomplished with only a single realization of the backscattering
far-field patterns averaged over the high-frequency band. |
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