  Background and Objective: Wilson statistics describe well the power spectrum
of proteins at high frequencies. Therefore, it has found several applications
in structural biology, e.g., it is the basis for sharpening steps used in
cryogenic electron microscopy (cryo-EM). A recent paper gave the first rigorous
proof of Wilson statistics based on a formalism of Wilson's original argument.
This new analysis also leads to statistical estimates of the scattering
potential of proteins that reveal a correlation between neighboring Fourier
coefficients. Here we exploit these estimates to craft a novel prior that can
be used for Bayesian inference of molecular structures. Methods: We describe
the properties of the prior and the computation of its hyperparameters. We then
evaluate the prior on two synthetic linear inverse problems, and compare
against a popular prior in cryo-EM reconstruction at a range of SNRs. Results:
We show that the new prior effectively suppresses noise and fills-in low SNR
regions in the spectral domain. Furthermore, it improves the resolution of
estimates on the problems considered for a wide range of SNR and produces
Fourier Shell Correlation curves that are insensitive to masking effects.
Conclusions: We analyze the assumptions in the model, discuss relations to
other regularization strategies, and postulate on potential implications for
structure determination in cryo-EM.
