An Algebraic Approach to Two-Dimensional Digital Image Restoration

Characteristical problem of multidimensional signal analysis and restoration is processing of extremely big amounts of data as well as handling of data dependancies in more than one direction. The problem of restoration can often be described as an ill-conditioned problem. In the following paper, an algebraic approach to two-dimensional image filtering will be presented. The Wiener solution will be extended to two-dimensional problem, introducing special formulation of an image signal matrix. The problem will be solved algebraically with twodimensional convolution filter implemented. There exist several different solutions of the Wiener normal equation problem, someof which are presented in this paper. Finally, the effectiveness of the suggested methods will be illustrated on some practical filtering problems. 1. The Image Degradation Model An imaging system can be generally represented as a continuous system with point-spread function h h x y f = ( , , , , ) ξ η and our distorted image will result from a convolution like g x y h x y f d d ( , ) ( , , , , ( , )) = −∞ ∞