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Image reconstruction in quantitative photoacoustic tomography with the simplified \(P_2\) approximation. (English) Zbl 1423.35441

Summary: Photoacoustic tomography (PAT) is a hybrid imaging modality that intends to construct high-resolution images of optical properties of heterogeneous media from measured acoustic data generated by the photoacoustic effect. To date, most of the model-based quantitative image reconstructions in PAT are performed with either the radiative transport equation or its classical diffusion approximation as the model of light propagation. In this work, we study quantitative image reconstructions in PAT using the simplified \(P_2\) equations as the light propagation model. We provide numerical evidences on the feasibility of this approach and derive some stability results as theoretical justifications.

MSC:

35R30 Inverse problems for PDEs
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65Z05 Applications to the sciences
74J25 Inverse problems for waves in solid mechanics
78A60 Lasers, masers, optical bistability, nonlinear optics
78A70 Biological applications of optics and electromagnetic theory
80A23 Inverse problems in thermodynamics and heat transfer

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References:

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