A Computational Introduction to Digital Image Processing, 2nd Edition

164 A Computational Introduction to Digital Image Processing, Second Edition

(a) Original image

(b) DFT of each row

of (a)

(c) DFT of each column

of (b)

FIGURE 7.7: Calculating a 2D DFT

where k is a scalar, and f and g are matrices. This follows directly from the definition given

in Equation 7.4.

This property is of great use in dealing with image degradation such as noise, which can

be modelled as a sum:

d = f + n

where f is the original image, n is the noise, and d is the degraded image. Since

F(d) = F(f ) + F(n)

we may be able to remove or reduce n by modifying the transform. As we shall see, some

noise appears on the DFT in a way that makes it particularly ...