具有部分数据和不确定光学参数的扩散超声调制生物发光断层成像
The Diffusive Ultrasound Modulated Bioluminescence Tomography with Partial Data and Uncertain Optical Parameters
AI总结：
针对部分边界测量且光学参数不确定的扩散超声调制生物发光断层成像，提出含不确定性量化的源重建与离散方法，并通过数值实验验证其有效性和可靠性。
摘要：
本文研究各向异性介质中具有部分边界测量的扩散超声调制生物发光断层成像的成像问题。在平面波调制假设下，我们将成像问题转化为一个具有内部数据的反问题，并推导了恢复生物发光源的重建流程。随后，建立了不确定性量化估计，以评估重建的鲁棒性。为便于实际实现，我们采用交错网格格式对扩散模型进行离散化，得到 UMBLT 反问题的离散表述。随后给出了离散重建流程以及离散不确定性量化估计。最后，通过数值算例对重建流程进行了定量验证，证明了所提方法和估计的有效性与可靠性。
英文摘要：
The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we 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. To facilitate practical implementation, we discretize the diffusive model using the staggered grid scheme, resulting in a discrete formulation of the UMBLT inverse problem. A discrete reconstruction procedure is then presented along with a discrete uncertainty quantification estimate. Finally, the reconstruction procedure is quantitatively validated through numerical examples to demonstrate the efficacy and reliability of the proposed approach and estimates.
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