Wiener Filters for the restoration of radiographs

In this paper, a new model of the radiologic process is developed. The model is based on a block diagram representation involving a nonlinear transformation. The optimal linear filter, in the mean square error sense (Wiener), retrieves information from a certain layer of the exposed object. It is derived by considering the contribution of the other layers as additive noise. Closed-form expressions are given for special cases to illustrate the filter behaviour for low and high frequencies. It is shown that the filter can be determined even if the focal spot is modelled as a point source. The effect of the distortion caused by the focal spot is found to be minimal compared to that of the superposition of the images produced by the other layers of the object. Experimental results show that optimal filtering exhibits improved performance over inverse filtering, which was previously used in a similar application.