A Model of the Image Restoration Process

A degradation function that, together with an additive noise term, operates on an input image f(x, y) to produce a degraded image g(x, y). Given g(x, y), some knowledge about the degradation function H, and come knowledge about the additive noise term η(x, y), the objective of restoration is to obtain an estimate f^(x, y) of the original image. We are estimating as close as possible to the original input image and, in general, the more we know about H and η, the closer f^(x ,y) will be to f(x, y). If H is a linear, positive-invariant process, then the degraded image is given in the spatial domain by    g (x, y) = h(x, y) * f(x, y) + η(x, y)