On the development of a Gaussian noise model for scatter compensation

The underlying mechanism in projection radiography as well as in computed tomography (CT) is the accumulative attenuation of a pencil x-ray beam along a straight line. However, when a portion of photons is deviated from their original path by scattering, it is not valid to assume that these photons are the survival photons along the lines connecting the x-ray source and the individual locations where they are detected. Since these photons do not carry the correct spatial information, the final image is contaminated. Researchers are seeking techniques to reduce scattering, and hence, improve image quality, by scatter compensation. Previously, we presented a post-acquisition scatter compensation technique based on an underlying statistical model. We used the Poisson noise model, which assumed that the signals in the detector individually followed the Poisson process. Since most x-ray detectors are energy integrating rather than photon counting, the Poisson noise model can be improved by taking this property into account. In this study, we developed a Gaussian noise model by the matching-of-the-first-two-moments method. The Maximum Likelihood Estimator of the scatter-free image was derived via the expectation maximization (EM) technique. The maximum a posteriori estimate was also calculated. The Gaussian noise model was preliminarily evaluated on a full-field digital mammography system.