Time-dependent angularly averaged inverse transport

TL;DR

This paper demonstrates the unique reconstruction and stability of absorption and scattering parameters in a time-dependent transport equation using boundary measurements, with a detailed analysis of measurement components.

Contribution

It introduces a method to uniquely determine and stably reconstruct absorption and scattering coefficients from angularly averaged boundary data in a time-dependent setting.

Findings

Unique determination of absorption and scattering coefficients.

Stability results for the reconstruction process.

Decomposition of measurements based on singular behavior.

Abstract

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. 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.