Cannon [1974] suggested a restoration filter R(u, υ)satisfying the conditionand based on t...

Cannon [1974] suggested a restoration filter R(u, υ)satisfying the condition

and based on the premise of forcing the power spectrum of the restored image, , to equal the power spectrum of the original image, |F(u, υ) |2. Assume that the image and noise are uncorrelated.

(a) Find R(u,υ)in terms of |F(u, υ) |2, |H(u, υ)|2,and |N(u,υ)|2. [Hint: Refer to Fig. 5.1, Eq. (5.5-17), and Problem 5.24.]

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(b) Use your result in (a) to state a result in the form of Eq. (5.8-2).

FIGURE 5.1

A model of the Image degradation/ restoration process.

5.24 Assume that the model in Fig. 5.1 is linear and position invariant and that the noise and image are uncorrelated. Show that the power spectrum of the output is

Refer to Eqs. (5.5-17) and (4.6-18).

FIGURE 5.1

A model of the image degradation/ restoration process.

(5.5-17)

(4.6-18)