Algorithms for Bayesian background-subtracted Fourier darkfield imaging

Formal consideration of prior information on the Fourier amplitude of background contrast in an image, using the same Bayesian principles of statistical inference which underlie thermodynamics, allows one to subtract background without favoring only selected parts of frequency space. Without the bias in frequency space which causes periodicity bleeding and mars literal interpretation of Fourier-filtered images, the shape transform of aperiodic objects can be left intact. Algorithms for Bayesian background subtraction from one- and two-dimensional images are presented which further consider, in ad hoc fashion, one's uncertainty about background amplitude. The results help explain the reported success of Fourier truncation, and indicate that Bayesian background-subtracted images can minimize root-mean-square image error, as well as periodicity bleeding, in comparison to Fourier-filtered and Fourier-truncated alternatives.