xxx.lanl.gov/abs/cond-mat/9711309
We show that Bayesian inference, like that used in statistical mechanics, can guide the systematic construction of Fourier dark-field methods for localizing periodicity in near-field (e.g. scanning-tunneling and electron-phase-contrast) images. For crystals in an aperiodic field, the Fourier coefficient Ze^{i phi} combines with a prior estimate for background amplitude B to predict background phase (beta) values distributed with a probability p(beta - phi | Z,phi,B) inversely proportional to the amplitude P of the signal of interest, when this latter is treated as an unknown translation scaled to B.
There are several project areas that spin off from here. One thread involves Bayesian background subtraction, the subject of a separate project topic here, especially for HREM and SPM images. The second in this vein involves extending the inference calculation to take into account other information, e.g. on background variances and co-variances.
Related projects planned for this map include Bayesian Background Subtraction, and Un-Biased Fourier Phase Estimation.