Image restoration using a two-dimensional Lorentzian probability model

It is known that the distribution of intensity gradients along separate horizontal and vertical directions in an image of a general scene often has a sharp peak with a long tail. This property, can be described by a Lorentzian probability function, and is the basis of an efficient nonlinear one-dimensional restoration algorithm. It can also superresolve a two-dimensional separable image. This paper discusses the gradient distribution in a general two-dimensional image and shows that the distribution of the maximum gradient at any picture point is also Lorentzian. This has been used to develop an iterative two-dimensional restoration algorithm. It starts by evaluating the likelihood of the intensity gradients within a Wiener filtered image. Then a nonlinear correction term is introduced which increases this likelihood under mean square error criterion. The method is applied to synthetic images and to a 94 GHz passive millimetre wave image. This new two-dimensional method is shown to be superior to the previous one-dimensional algorithm which had to be applied separately along two orthogonal directions.