标题： Lippmann-Schwinger-Lanczos 方法求解共振频率域中薛定谔方程的逆散射问题 显示英文标题

标题： Lippmann-Schwinger-Lanczos approach for inverse scattering problem of Schrodinger equation in the resonance frequency domain

摘要： 在Lippmann-Schwinger-Lanczos（LSL）方法中，已经成功地利用扩散频率域中的数据获得了薛定谔方程势的重构，但远离传感器位置的有限分辨率导致图像模糊不清。为了改进重构效果，本研究将该方法的应用范围扩展到了共振频率域的数据。我们根据Weyl定律提出了一种特定的数据采样方式，能够在不过度采样的情况下获得清晰图像，并且避免了计算复杂度的急剧增加。最后展示的数值结果展示了该算法的性能。 显示英文摘要

摘要： Reconstructions of potential in Schrodinger equation with data in the diffusion frequency domain have been successfully obtained within Lippmann-Schwinger-Lanczos (LSL) approach, however limited resolution away from the sensor positions resulted in rather blurry images. To improve the reconstructions, in this work we extended the applicability of the approach to the data in the resonance frequency domain. We proposed a specific data sampling according to Weyl's law that allows us to obtain sharp images without oversampling and overwhelming computational complexity. Numerical results presented at the end illustrate the performance of the algorithm.