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

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