Inverse Transport and Diffusion Problems in Photoacoustic Imaging with Nonlinear Absorption
Inverse Transport and Diffusion Problems in Photoacoustic Imaging with Nonlinear Absorption
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DOI：
10.1137/21m1436178
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Ru-Yu Lai;Kui Ren;Ting Zhou
中科院分区：
文献类型：
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作者：
Ru-Yu Lai;Kui Ren;Ting Zhou
基于光声层析成像技术在非线性光学吸收成像中的应用，本文研究了一个半线性辐射输运方程的系数反问题及其扩散近似问题，其内部数据是系数和方程解的泛函。基于一阶二阶线性化技术，我们得到了反问题的唯一性和稳定性结果。为了不确定量化的目的，我们还建立了吸收系数重构相对于散射系数变化的稳定性。
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 firstand secondorder 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.