  We consider the inverse random potential scattering problem for the two- and
three-dimensional biharmonic wave equation in lossy media. The potential is
assumed to be a microlocally isotropic Gaussian rough field. The main
contributions of the work are twofold. First, the unique continuation principle
is proved for the fourth order biharmonic wave equation with rough potentials
and the well-posedness of the direct scattering problem is established in the
distribution sense. Second, the correlation strength of the random potential is
shown to be uniquely determined by the high frequency limit of the second
moment of the scattered field averaged over the frequency band. Moreover, we
demonstrate that the expectation in the data can be removed and the data of a
single realization is sufficient for the uniqueness of the inverse problem with
probability one when the medium is lossless.

Analysis of PDEs