Digital Signal Processing Reference
In-Depth Information
Stage 2. Image Restoration
a.
The restoration is done by passing the degraded image
y
(
n
1
, n
2)
through a restoring filter
g
(
n
1
, n
2). Determine the 16
16 restored
image matrices
x
1(
n
1
, n
2) and
x
2(
n
1
, n
2)
,
respectively, for the fol-
lowing filters:
×
1
(
)
=
•
Inverse filter:
G
ωω
,
(
)
12
H
ωω
,
12
(
)
H
*
ωω
,
(
)
=
12
•
Wiener filter:
G
ωω
,
12
(
)
2
N
ωω
,
(
)
2
12
H
ωω
,
+
12
(
)
2
X
ωω
,
12
where the symbol * denotes complex conjugate.
b.
For comparison, determine the relative error of transmission
et
=
100
×
norm(
e
)/norm(
x
) in the following cases:
•
Without any restoring filter:
e
(
n
1
,
n
2
) =
y
(
n
1
,
n
2
) -
x
(
n
1
,
n
2
)
•
With inverse filter:
e
(
n
1
,
n
2
) =
x
1
(
n
1
,
n
2
) -
x
(
n
1
,
n
2
)
•
With Wiener filter:
e
(
n
1
,
n
2
) =
x
2
(
n
1
,
n
2
) -
x
(
n
1
,
n
2
)
Stage 3. Thresholding of Images and Display
We can apply the thresholding process to an image
x
(
n
1
, n
2) and obtain a
display image
xt
(
n
1
, n
2
) as follows:
% MATLAB Program to Apply Thresholding on Filtered Image
for n1= 1:16
for n1= 1:16
if abs(x(n1, n2)) > T xt(n1, n2) = '*'
else xt(n1, n2) = ' '
end
end
end
Apply the thresholding process to the following images, and display them
by using a threshold level of
T
= 0.5.
•
The original picture
x
(
n
1
,
n
2
)
•
The restored image
x
1
(
n
1
,
n
2
) obtained by inverse filtering
•
The restored image
x
2
(
n
1
,
n
2
) obtained by Wiener filtering
