论文标题
部分可观测时空混沌系统的无模型预测
Shape reconstructions by using plasmon resonances with enhanced sensitivity
论文作者
论文摘要
本文研究了横向电磁散射中近场测量值的子波长对象的形状重建。这个几何逆问题众所周知，这是不适的和具有挑战性的。我们使用具有显着增强的灵敏度和分辨率的等离子体共振来开发一种新型的重建方案。首先，通过光谱分析，我们在重建的灵敏度与等离子共振之间建立了急剧的定量关系。它表明，当引起等离子体共振时，灵敏度功能会爆炸。因此，信噪比显着提高，并确保重建的鲁棒性和有效性。其次，提出了一种差异正则化方法来克服未适应性，并引入了交替的迭代方法以自动选择正则化参数。第三，我们使用拉普拉斯近似方法捕获目标散射对象的统计信息。进行严格的理论分析和广泛的数值实验，以验证我们方法的有希望的特征。
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel reconstruction scheme using plasmon resonances with significantly enhanced sensitivity and resolution. First, by spectral analysis, we establish a sharp quantitative relationship between the sensitivity of the reconstruction and the plasmon resonance. It shows that the sensitivity functional blows up when plasmon resonance occurs. Hence, the signal-to-noise ratio is significantly improved and the robustness and effectiveness of the reconstruction are ensured. Second, a variational regularization method is proposed to overcome the ill-posedness, and an alternating iteration method is introduced to automatically select the regularization parameters. Third, we use the Laplace approximation method to capture the statistical information of the target scattering object. Both rigorous theoretical analysis and extensive numerical experiments are conducted to validate the promising features of our method.
