Write brief notes on inverse filtering.
The simplest approach to restoration is direct inverse filtering, where F (u, v), the transform of the original image is computed simply by dividing the transform of the degraded image, G (u, v), by the degradation function
The divisions are between individual elements of the functions.
But G (u, v) is given by
G (u, v) = F (u, v) + N (u, v)
Hence
It tells that even if the degradation function is known the undegraded image cannot be recovered [the inverse Fourier transform of F( u, v)] exactly because N(u, v) is a random function whose Fourier transform is not known.
If the degradation has zero or very small values, then the ratio N(u, v)/H(u, v) could easily dominate the estimate F(u, v).
One approach to get around the zero or small-value problem is to limit the filter frequencies to values near the origin. H (0, 0) is equal to the average value of h(x, y) and that this
is usually the highest value of H (u, v) in the frequency domain. Thus, by limiting the analysis to frequencies near the origin, the probability of encountering zero values is reduced.
