2 research outputs found
Time-dependent angularly averaged inverse transport
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
Inverse Transport Theory of Photoacoustics
We consider the reconstruction of optical parameters in a domain of interest
from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency
electromagnetic waves into the domain and measures acoustic signals emitted by
the resulting thermal expansion. Acoustic signals are then used to construct
the deposited thermal energy map. The latter depends on the constitutive
optical parameters in a nontrivial manner. In this paper, we develop and use an
inverse transport theory with internal measurements to extract information on
the optical coefficients from knowledge of the deposited thermal energy map. We
consider the multi-measurement setting in which many electromagnetic radiation
patterns are used to probe the domain of interest. By developing an expansion
of the measurement operator into singular components, we show that the spatial
variations of the intrinsic attenuation and the scattering coefficients may be
reconstructed. We also reconstruct coefficients describing anisotropic
scattering of photons, such as the anisotropy coefficient in a
Henyey-Greenstein phase function model. Finally, we derive stability estimates
for the reconstructions