Bayesian Restoration of Medical X-Ray Digital Images

Image entropy as prior in Bayesian inference was applied to the restoration of X-ray digital images with additive zero mean Gaussian distributed noise. An iterative algorithm based on a conjugate gradient method with numerical evaluation of partial derivatives was developed to efficiently minimize the potential function associated to any positive, additive distribution. The correlation matrix of the errors, both in the data acquisition and the modeling process, was built up and used as prior in Bayesian approach. Digitized and digitally acquired X-ray mammograms were subject of comparative analyses before and after running the algorithm. All output images displayed better overall quality as compared with their input counterparts in terms of contrast, signal to noise ratio, and visibility of details. No artifacts were detected by all means as being introduced by the entropic method, which theoretically ensures the least biased and structureless output image restoration. Key-Words: Bayesian inference, Maximum entropy principle, Inverse problem, X-ray digital image