Reconstructions of potential in Schrödinger equation with data in the diffusion frequency domain have been successfully obtained within Lippmann-Schwinger-Lanczos (LSL) approach in Baker et al. (Regularized reduced order Lippmann-Schwinger-Lanczos method for inverse scattering problems in the frequency domain (submitted). J. Comput. Phys. https://arxiv.org/abs/2311.16367 ), 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.