The paper studies an imaging problem in diffusive ultrasound-modulated bioluminescence tomography (UMBLT) with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, the authors transform the imaging problem to an inverse problem with internal data and derive a reconstruction procedure to recover the bioluminescent source. Subsequently, an uncertainty quantification estimate is established to assess the robustness of the reconstruction.
The key highlights and insights are:
Reconstruction in Optically Anisotropic Media: The authors generalize the reconstruction procedure for diffusive UMBLT to optically anisotropic media, providing a more comprehensive understanding of UMBLT imaging in complex media.
Reconstruction with Partial Data: The authors extend the reconstruction procedure to the case where data is only available on a partial boundary, furnishing a theoretical underpinning for source imaging with limited data acquisition.
Uncertainty Quantification: The authors derive a quantitative uncertainty estimate using the PDE theory of second-order elliptic equations, demonstrating how the variance of the source is linked to the variance of the optical parameters.
Discrete Formulation: The authors discretize the diffusion equation using the staggered grid scheme to yield a discrete formulation of the UMBLT inverse problem, facilitating numerical implementation and validation.
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소스 콘텐츠 기반
arxiv.org
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