2021/07/16 by Ru-Yu Lai, Kui Ren, Lai, Ru-Yu +3 · 1 citation
Engineering · Medicine · #Advanced X-ray and CT Imaging #Analysis of PDEs (math.AP) #FOS: Mathematics #Optical Imaging and Spectroscopy Techniques #Photoacoustic and Ultrasonic Imaging
paper · pdf · doi:10.48550/arxiv.2107.08118
openalex publication_date 2021/07/16 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28
Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography (PAT), 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 purpose, we also establish the stability of the reconstruction of the absorption coefficients with respect to the change in the scattering coefficient.