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Time-dependent angularly averaged inverse transport. (English) Zbl 1177.35246

Summary: This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. Such measurement settings find applications in medical and geophysical imaging. We show that the absorption coefficient and the spatial component of the scattering coefficient are uniquely determined by such measurements. We obtain stability results on the reconstruction of the absorption and scattering parameters with respect to the measured albedo operator. The stability results are obtained by a precise decomposition of the measurements into components with different singular behavior in the time domain.

MSC:

35R30 Inverse problems for PDEs
35B35 Stability in context of PDEs
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
92C50 Medical applications (general)
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