Image restoration is the process employed to “compensate for” or “undo” defects which degrade an image. Image Degradation occurs in many forms such as motion blur, noise, and camera mis focus. Especially in cases like motion blur, it is possible to come up with a very good estimate of the actual blurring function and “undo” the blur to restore the original image. In cases where the image is corrupted by noise, the best we may hope to do is to compensate for the degradation it caused. A general block diagram of a degradation model is shown in Figure 1.
Degradation Model for Continuous Function
If an image f(x,y) is to be convolved with the two-dimensional impulse function δ(x,y), then it can be expressed as:
f(x,y)=∫−∞∞ ∫∞−∞ f(x, y)δ(x-x0, y-y0)dxdy(1)Using dummy variables α and β, we can represent
f(x,y)=∫∞−∞∫∞−∞ f(α,β)δ(x-a,y-β)dαdβ(2)Now,g(x,y)=H[f(x,y)]+w(x,y)(3) and
H=[∫∞−∞ ∫∞−∞f(α,β)δ(x-α,y-β)dαdβ]+w(x,y)(4)Using H as linear operator, we can write
g(x,y)=∫∞−∞∫∞−∞H[f(α,β)δ(x-α,y-β)dαdβ]+w(x,y)(5)As we know that f (α,β) is independent of x and y and hence, by applying the homogeneity property, the Equation can be expressed as:
g(x,y)=∫∞−∞∫∞−∞ f(α,β)H[δ(x-α,y-β)dαdβ]+w(x,y)(6)When
h(x,α,y,β) = H[δ(x-α,y-β)]
Then,
g(x,y)=∫∞−∞∫∞−∞f(α,β)h(x,α,y,β)dαdβ]+w(x,y)(7)The equation for degradation model for continuous image function f(x,y).