Image Restoration Using a Lorentzian Probability Model

Abstract

The distribution of edge values for an image of a general scene often has a sharp peak with a long tail. This property, which can be well described by a Lorentzian probability function, has been used to develop an efficient nonlinear image restoration algorithm for reducing the various artifacts that often arise in the restored images. The algorithm starts with a Wiener filter solution which is used to model the edge image by the Lorentzian function so that the likelihood of the image can be estimated. A nonlinear correction term is then introduced which increases this image likelihood under the mean square error criterion. This process ensures that the resulting image retains its sharpness while reducing the noise and ringing artifacts. An iterative procedure has been developed to implement this method. Computer simulated results show that the algorithm is robust in reducing artifacts and easily implemented. The algorithm also possesses a superresolution capability due to the highly nonlinear property of the correction term.