i. The principal goal of restoration techniques is to improve an image in some predefined sense. Restoration attempts to recover an image that has been degraded, by using a priori knowledge of the degradation phenomenon.

ii. Thus restoration techniques are oriented towards modeling the degradation and applying the inverse process in order to recover the original image.

iii. As Fig. 1 shows, the degradation process is modeled as 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).

iv. Given g(x, y), some knowledge about the degradation function H, and some knowledge about the additive noise term f(x, y), the objective of restoration is to obtain an estimate f(x, y) of the original image.

v. We want the estimate to be as close as possible to the original input image and, in general, the more we know about H and f, the closer f(x, y) will be to f(x, y).

vi. The restoration approach used mostly is based on various types of image restoration filters

vii. We know that if H is a linear, position-invariant process, then the degraded image is given in the spatial domain by

$g(x, y) = h(x, y)* f(x, y) + 77(x, y) \space\space\space\space\space\space Eq.(1) $

Where h(x, y) is the spatial representation of the degradation function and the symbol "*" indicates convolution.

viii. Now, convolution in the spatial domain is analogous to multiplication in the frequency domain, so we may write the model in Eq. (1) in an equivalent frequency domain representation:

$G(u, v) = H (u, v)F(u, v) + N(u, v) \space\space\space\space\space\space Eq.(2)$

ix. Where the terms in capital letters are the Fourier transforms of the corresponding terms in Eq. (1). These two equations are the bases for most of the restoration material.

x. This is about the basic image restoration model.