| Abstract: |
| In this talk, we explore the numerical analysis of quantitative photoacoustic tomography, modeled as an inverse problem to reconstruct the diffusion and absorption coefficients in a second-order elliptic equation using multiple internal measurements. We establish conditional stability in the $L^2$ norm, under a provable nonzero condition, with randomly chosen boundary excitation data. Building on this stability, we propose and analyze a numerical reconstruction scheme based on an output least-squares formulation, using finite element discretization. We provide an \textit{a priori} error estimate for the numerical reconstruction, serving as a guideline for selecting algorithmic parameters. Several numerical examples will be presented to illustrate the theoretical results. |
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