Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography, we study in this work inverse coefficient problems for a semilinear radiative transport equation and its diffusion approximation with internal data that are functionals of the coefficients and the solutions to the equations. Based on the techniques of first- and second-order linearization, we derive uniqueness and stability results for the inverse problems. For uncertainty quantification purposes, we also establish the stability of the reconstruction of the absorption coefficients with respect to the change in the scattering coefficient.
Bibliographical noteFunding Information:
\ast Received by the editors July 26, 2021; accepted for publication (in revised form) December 14, 2021; published electronically April 14, 2022. https://doi.org/10.1137/21M1436178 Funding: This work is partially supported by the National Science Foundation through grants DMS-1937254, DMS-1913309, and DMS-2006731. \dagger School of Mathematics, University of Minnesota, Minneapolis, MN 55455 USA (firstname.lastname@example.org). \ddagger Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 USA (email@example.com). \S Department of Mathematics, Northeastern University, Boston, MA 02115 USA (t.zhou@ northeastern.edu).
© 2022 Society for Industrial and Applied Mathematics
- inverse coefficient problem
- inverse diffusion
- quantitative photoacoustic imaging
- semilinear radiative transport
- uncertainty quantification
- uniqueness and stability