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.

翻译：在扩散频率域数据下，利用Lippmann-Schwinger-Lanczos（LSL）方法已成功实现了薛定谔方程中势函数的重构，但远离传感器位置的分辨率限制导致图像较为模糊。为改进重构效果，本研究将该方法的适用范围扩展至共振频率域数据。我们依据外尔定律提出了一种特定的数据采样方案，使得在不进行过采样且不产生过高计算复杂度的前提下能够获得清晰图像。文末给出的数值结果验证了该算法的性能。