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53
12
11
10
10
Power spectrum
8
6
4
2
0
Power spectrum
9
8
7
6
5
4
−2
0 0.1 0.2 0.3 0.4 0.5
Normalized frequency
3
0 0.1 0.2 0.3 0.4 0.5
Normalized frequency
Figure 3.10 – (Left) Power spectrum computed directly on the noisy image, frequncies
of striping are not visible (Right) Power spectrum computed as an average of the columns
periodograms ; striping frequencies appear as distinct peaks
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
u
u
v
v
Figure 3.11 – Frequency response of the filter H 1 . As the value of σ increases, the wells
(represented here as lobes for visual clarity) overlap. When frequencies located near the
center of fourier domain are reached by the lobes, the band-pass filter H 1 becomes a high
pass filter
takes the form :
H 1 (u, v) =1− ∑
(u s,v s)
exp
(− (u − u s) 2 +(v − v s ) 2 )
σ 2
(3.17)
where u s and v s are the center coordinates of the wells in the fourier domain and σ
controls the sharpness of the wells. The design of the FIR filter H 1 in the fourier 2D
domain, implicitly takes into account the unidirectional spatial property of stripes noise
by placing the wells along the vertical axis, centered at the same coordinates as the stripe
lobes observed in figure 3.8. With increasing values of σ, the wells start to overlap with
each other and eventually affect low-frequencies (figure 3.11b). For high values of σ, the
filter H 1 shifts from a band-pass filter to a high-pass filter that removes all the low-pass