ECE468: HOMEWORK 5
due 02/19
•Problem 1 (50pts)
The ability to simulate the effect of noise in images is central to understanding image restoration.
Write a MATLAB code for corrupting an input image with additive noise. Use the image that is
available on the class website as input. Your report should include:
1) M-file with a well commented code;
2) Figure 1: input image corrupted with Gaussian noise with mean 64, and variance 400;
3) Figure 2: input image corrupted with salt-and-pepper noise, so that on average 8% of the image
contains the noise;
4) Figure 3: input image corrupted with exponential noise with mean 1
a, where a= 0.1. To this end,
use the theoretical result that if a random variable, η, has the uniform distribution, η∼U(0,1),
then ν=−1
aln(1−η)has the exponential distribution with mean 1
a, i.e., ν∼aexp(−aν),ν≥0.
(Hint: Use ’imnoise’, ’randn’, ’rand’)
•Problem 2 (50pts)
Write a MATLAB code for filtering the noise-corrupted images from Problem 1. Your report should
include:
1) M-file with a well commented code;
2) Figures 4, 5, 6: the result of filtering Figures 1, 2, 3 with the median spatial filter with size
Sxy = 7 ×7;
3) Figure 7, 8, 9: the result of filtering Figures 1, 2, 3 with the adaptive filter defined by equation
(5.3-12) in the textbook, with size Sxy = 7 ×7; You cannot assume that you know the mean
and variance of noise in the images.
(Hint: Use ’medfilt2’. To design the adaptive filter (5.3-12), you first need to estimate the
arithmetic mean mLand variance σ2
Lof the region Sxy on which the filter is applied. Then, you
need to guess the variance of noise in the images. Read carefully the textbook instructions on
page 331.)