On recovery of an inhomogeneous cavity in inverse acoustic scattering
Fenglong Qu Jiaqing Yang
Inverse Problems & Imaging 2018, 12(2): 281-291 doi: 10.3934/ipi.2018012

Consider the time-harmonic acoustic scattering of an incident point source inside an inhomogeneous cavity. By constructing an equivalent integral equation, the well-posedness of the direct problem is proved in $L^p$ with using the classical Fredholm theory. Motivated by the previous work [10], a novel uniqueness result is then established for the inverse problem of recovering the refractive index of piecewise constant function from the wave fields measured on a closed surface inside the cavity.

keywords: Uniqueness inverse scattering refractive index inhomogeneous cavity point source
Reconstruction of penetrable grating profiles
Jiaqing Yang Bo Zhang Ruming Zhang
Inverse Problems & Imaging 2013, 7(4): 1393-1407 doi: 10.3934/ipi.2013.7.1393
This paper is concerned with the inverse problem of recovering a penetrable grating profile in the TM-polarization case from the scattered field measured only above the structure, corresponding to a countably infinite number of incident quasi-periodic waves. A sampling method is proposed to reconstruct the penetrable grating profile based on a near field linear operator equation in $l^2$. The mathematical justification of the sampling method is established and numerical results are presented to show the validity of the inversion algorithm.
keywords: grating profile Sampling method transmission condition quasi-periodic boundary value problem impedance Green's function.

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