Lipschitz stability at the boundary for time-harmonic diffuse optical\n tomography

2020/02/05 by Olga Doeva, Romina Gaburro, Doeva, Olga +5
Mathematics · Engineering · Medicine · #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Optical Imaging and Spectroscopy Techniques

paper · pdf · doi:10.48550/arxiv.2002.01828

Abstract

We study the inverse problem in Optical Tomography of determining the optical\nproperties of a medium \Ω\⊂\ℝⁿ, with n\≥ 3, under the\nso-called diffusion approximation. We consider the time-harmonic case where\n\Ω is probed with an input field that is modulated with a fixed harmonic\nfrequency \ω=\(k)/(c), where c is the speed of light and k is the\nwave number. We prove a result of Lipschitz stability of the absorption\ncoefficient \μ_a at the boundary \∂\Ω in terms of the\nmeasurements in the case when the scattering coefficient \μ_s is assumed to\nbe known and k belongs to certain intervals depending on some a-priori bounds\non \μ_a, \μ_s.\n

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