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Analysis of the linearized problem of quantitative photoacoustic tomography. (English) Zbl 1383.65013

Summary: Quantitative image reconstruction in photoacoustic tomography requires the solution of a coupled physics inverse problem involving light transport and acoustic wave propagation. In this paper we address this issue employing the radiative transfer equation as an accurate model for light transport. As main theoretical results, we derive several stability and uniqueness results for the linearized inverse problem. We consider the case of single illumination as well as the case of multiple illuminations assuming full or partial data. The numerical solution of the linearized problem is much less costly than the solution of the nonlinear problem. We present numerical simulations supporting the derived stability results for the linearized problem of quantitative photoacoustic tomography.

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
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