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Quantitative image reconstruction in photoacoustic tomography requires the solution of a coupled physics inverse problem involvier light transport and acoustic wave propagation. In this paper we address this issue employing the radiative transfer equation as 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 non-linear problem. We present numerical simulations supporting the stability results for the linearized problem and demonstrate that the linearized problem already gives accurate quantitative results.
The development of accurate and efficient image reconstruction algorithms is a central aspect of quantitative photoacoustic tomography (QPAT). In this paper, we address this issues for multi-source QPAT using the radiative transfer equation (RTE) as
We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photo- and thermoacoustic tomography an
We analyze the mathematical model of multiwave tomography with a variable speed with integrating measurements on planes tangent to a sphere surrounding the source. We prove sharp uniqueness and stability estimates with full and partial data and propo
We study the well-posedness theory for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors in the La
Here we present a novel microlocal analysis of a new toric section transform which describes a two dimensional image reconstruction problem in Compton scattering tomography and airport baggage screening. By an analysis of two separate limited data pr