Deblurring the discrete Gaussian blur

Abstract

In 1995 Z. Reti presented a method for deblurring images blurred by the discrete Gaussian. The method is based on theorems borrowed from analytic number theory developed by Gauss, G. Jacobi (1829), and Ramanujan. One advantage of this method over similar ones developed for the continuous domain is that it provides exact formulas for the deblurring convolution. In addition, while deblurring the Gaussian in the continuous domain is an ill-posed inverse problem, deblurring the discrete Gaussian model results in a mathematically well-posed problem. The formulas presented here provide error bounds which relate the quality of the reconstructed image to that of the blurred image. This deblurring method is conveniently expressed in terms of multiplication by Toeplitz matrices whose diagonal entries decrease exponentially, thus rendering the method suitable for numerical approximations. Condition numbers are provided for various choices of /spl sigma/.