English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate the asymptotic relation between the inverse problems relyingon the Helmholtz equation and the radiative transfer equation (RTE) as physicalmodels, in the high-frequency limit. In particular, we evaluate the asymptoticconvergence of a generalized version of inverse scattering problem based on theHelmholtz equation, to the inverse scattering problem of the Liouville equation(a simplified version of RTE). The two inverse problems are connected throughthe Wigner transform that translates the wave-type description on the physicalspace to the kinetic-type description on the phase space, and the Husimitransform that models data localized both in location and direction. Thefinding suggests that impinging tightly concentrated monochromatic beams canindeed provide stable reconstruction of the medium, asymptotically in thehigh-frequency regime. This fact stands in contrast with the unstablereconstruction for the classical inverse scattering problem when the probingsignals are plane-waves.

High-frequency limit of the inverse scattering problem: asymptotic convergence from inverse Helmholtz to inverse Liouville