Abstract
AbstractWe propose a reliable direct imaging method based on the reverse time migration for finding extended obstacles with phaseless total field data. We prove that the imaging resolution of the method is essentially the same as the imaging results using the scattering data with full phase information when the measurement is far away from the obstacle. The imaginary part of the cross-correlation imaging functional always peaks on the boundary of the obstacle. Numerical experiments are included to illustrate the powerful imaging quality
Highlights
We consider in this paper inverse scattering problems with phaseless data which aim to find the support of unknown obstacles embedded in a known background medium from the knowledge of the amplitude of the total field measured on a given surface far away from the obstacles
The condition (1.3) is the outgoing Sommerfeld radiation condition which guarentees the uniqueness of the solution
For the sake of the simplicity, we mainly consider the imaging of sound soft obstacles in this paper
Summary
We consider in this paper inverse scattering problems with phaseless data which aim to find the support of unknown obstacles embedded in a known background medium from the knowledge of the amplitude of the total field measured on a given surface far away from the obstacles. Let ui be the incident wave and the total field is u = ui + us with us being the solution of the following acoustic scattering problem:. We introduce the RTM method for inverse scattering problems with phaseless data. We assume the obstacle D ⊂ Ω and Ω is inside Bs, Br. is the fundamental solution of the Helmholtz equation with the source at xs ∈ Γs, be the incident wave and |u(xr, xs)| = |us(xr, xs) + ui(xr, xs)| be the phaseless data received at xr ∈ Γr, where us(x, xs) is the solution to the problem (1.1)-(1.3) with ui(x, xs) = Φ(x, xs).
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