Application of Polynomial Transforms in Image Deblurring
Jean-Bernard Martens · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1989
In this paper, we present an algorithm for deblurring and interpolating digital images. Deblurring is an ill-posed problem, which can be made well-behaved by introducing assumptions about the input image. The algorithm described in this paper assumes that images can be described by local polynomial expansions. The mapping between an image and the coefficients of the polynomial approximation is called a polynomial transform. It is shown that, by using this image approximation, deblurring becomes equivalent to estimating the polynomial transform coefficients of the image. In practice, the noise and sampling of the blurred image limit the order of the coefficients that can be estimated reliably.