Applications of digital signal processing - Continuous and Discrete Time Signals and Systems - page 778

Fig. 17.20. (a) Ayantika image
corrupted with high-frequency
noise. The noise appears as
vertical and horizontal lines in
the image. (b) Power spectrum
of the Ayantika image.

1

0.5

0

0

p

0.5 p

−0.5 p

0

−0.5 p

− p

(a) (b)

17.6.1 Lowpass filtering

Lowpass filtering is widely used in many image processing applications. Some
applications include reducing high-frequency noise that is corrupting an image,
band-limiting the frequency component of an image prior to decimation, and
smoothing the rough edges of an image. In Example 17.9 we provide an example
of lowpass filtering in the spatial domain.

Example 17.9
Figure 17.20(a) shows a noise-corrupted image, referred to as Ayantika. Show
that:

(a) the image has high-frequency noise by plotting the power spectrum;
(b) the lowpass filter with the following impulse response:

12321
23432
34543
23432
12321

1
64

h [ m , n ] = (17.27)

eliminates the high-frequency noise from the image.

Solution
The M ATLAB code used to plot the power spectrum is given by

>> I = imread('ayantika.tif');
>> I = double(I);
>>I=I-mean(mean(I));