  This paper 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.
