  We investigate the asymptotic relation between the inverse problems relying
on the Helmholtz equation and the radiative transfer equation (RTE) as physical
models, in the high-frequency limit. In particular, we evaluate the asymptotic
convergence of a generalized version of inverse scattering problem based on the
Helmholtz equation, to the inverse scattering problem of the Liouville equation
(a simplified version of RTE). The two inverse problems are connected through
the Wigner transform that translates the wave-type description on the physical
space to the kinetic-type description on the phase space, and the Husimi
transform that models data localized both in location and direction. The
finding suggests that impinging tightly concentrated monochromatic beams can
indeed provide stable reconstruction of the medium, asymptotically in the
high-frequency regime. This fact stands in contrast with the unstable
reconstruction for the classical inverse scattering problem when the probing
signals are plane-waves.
