Image Restoration

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Chapter 5 Image Restoration
Goal of Restoration Improve an image in some
predefined sense. i.e. g(x,y)h(x,y)f(x,y)?(x,
y) G(u,v)H(u,v)F(u,v)N(u,v)
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This test pattern is well-suited for illustrating
the noise models, because it is composed of
simple, constant areas that span the grey scale
from black to white in only three increments.
This facilitates visual analysis of the
characteristics of the various noise components
added to the image.
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Periodic Noise Reduction by Frequency Domain
Filtering

• LPF HPF ? Image Enhancement
• Bandreject Filters
• 1-1) Ideal

D(u,v) distance from the origin of the centered
frequency rectangle W bandwidth D0 radial
center
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Periodic Noise Reduction by Frequency Domain
Filtering
1-2) Butterworth of order n
1-3) Gaussian
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Periodic Noise Reduction by Frequency Domain
Filtering

• Bandreject Filters
• Hbp(u,v)1-Hbr(u,v)
• It helps isolate the noise pattern.

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Periodic Noise Reduction by Frequency Domain
Filtering
3) Notch Filters 3-1) Ideal
The center of the frequency rectangle has been
shifted to the point (M/2,N/2)
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Periodic Noise Reduction by Frequency Domain
Filtering Notch Filters
3-2) Butterworth of order n
3-3) Gaussian
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Periodic Noise Reduction by Frequency Domain
Filtering
4) Optimum Notch Filters
To obtain w(x,y) the goal is to minimize the
variance in the neighborhood of x,y in the image.
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Linear, Position-Invariant Degradations
Estimation the Degradation Function 1) Estimation
by Image Observation
Assuming that the effect of noise is negligible.
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Linear, Position-Invariant Degradations
Estimation the Degradation Function 2) Estimation
by Experimentation
A impulse Fourier transform which is constant.
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Linear, Position-Invariant Degradations
Estimation the Degradation Function 3) Estimation
by modeling Turbulence model Mathematical
model
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• How to get F(u,v) from degraded image G(u,v)
• Inverse Filtering

We should know N(u,v) to use this method. We
should use this method near origin because H(u,v)
is near zero in other areas.
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How to get F(u,v) from degraded image G(u,v)
2) Wiener (Minimum mean square Error) Filtering
H(u,v) degradation function Sn(u,v)N(u,v)2 po
wer spectrum of the noise Sf(u,v)F(u,v)2 power
spectrum of the undergraded image
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If Sf(u,v) is not known
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How to get F(u,v) from degraded image G(u,v)
3) Constrained Least Squares Filtering
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• Geometric Transformations (rubber-sheet
  transformations)
• 1) Spatial Transformations
• 2) Gray-level Transformations

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