利用等离子体共振进行形状重建
Shape reconstructions by using plasmon resonances
摘要：
本文研究了由伴随电场的远场测量重建夹杂物的形状。这是一个在生物医学成像中具有实际重要性的逆问题，并且众所周知是病态的。通过将Drude的介电常数参数模型，我们提出了一种新的重建方案，通过使用等离子体共振显着增强的谐振场。我们进行了精细的灵敏度分析，以建立重建的灵敏度和等离子体共振之间的尖锐关系。它示出，当等离子体共振发生时，灵敏度功能爆破，从而确保一个更强大和有效的建设。然后我们将Tikhonov正则化与Laplace近似相结合来求解反问题，这是确定性和随机性方法的有机杂交，可以快速计算极小值，同时捕获解的不确定性。我们进行了广泛的数值实验来说明所提出的重建方案的有前途的功能。
英文摘要：
We study the shape reconstruction of an inclusion from the {faraway} measurement of the associated electric field. This is an inverse problem of practical importance in biomedical imaging and is known to be notoriously ill-posed. By incorporating Drude's model of the permittivity parameter, we propose a novel reconstruction scheme by using the plasmon resonance with a significantly enhanced resonant field. We conduct a delicate sensitivity analysis to establish a sharp relationship between the sensitivity of the reconstruction and the plasmon resonance. It is shown that when plasmon resonance occurs, the sensitivity functional blows up and hence ensures a more robust and effective construction. Then we combine the Tikhonov regularization with the Laplace approximation to solve the inverse problem, which is an organic hybridization of the deterministic and stochastic methods and can quickly calculate the minimizer while capture the uncertainty of the solution. We conduct extensive numerical experiments to illustrate the promising features of the proposed reconstruction scheme.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
