For general d-dimensional distributions, heavy-hitter reconstruction from Fourier coefficients requires and suffices with roughly exp(sqrt(d)) coefficients, versus exp(d) for Wasserstein distance.
Superresolution without separation.Information and Inference: A Journal of the IMA, 7(1):1–30, 2018
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Model-agnostic super-resolution in high dimensions
For general d-dimensional distributions, heavy-hitter reconstruction from Fourier coefficients requires and suffices with roughly exp(sqrt(d)) coefficients, versus exp(d) for Wasserstein distance.