As a matter of fact, the Wiener filter is most popular filter and is used for restoration. The main limitation of the earlier discussed methods viz., Inverse filtering and Pseudo-Inverse filtering is that they are sensitive to noise (The Wiener filter exploits the statistical properties of the image and can be used to restore images in the presence of blur as well as noise. Let f(x, y), g(x, y) and f(x, y) be zero mean random sequences. Zero-mean sequences imply E[f(x, y)] = 0, E[g(x, y)] = 0 and E[f(x, y)] = 0. Similarly, stationary sequences can be defined in terms of correlation as under: E[ƒ (x, y).ƒ (i, j)]=rf ( x − i, y − 1) | E[g (x, y).g (i, j)] = rgg (x-i, y-j) f 88 → Auto correlation Elf (x, y). g(i, j)] = g(x-i, yj) → cross correlation The zero mean image model is given by the following expression. List the major drawbacks of Wieners filter.
As a matter of fact, the Wiener filter is most popular filter and is used for restoration. The main limitation of the earlier discussed methods viz., Inverse filtering and Pseudo-Inverse filtering is that they are sensitive to noise (The Wiener filter exploits the statistical properties of the image and can be used to restore images in the presence of blur as well as noise. Let f(x, y), g(x, y) and f(x, y) be zero mean random sequences. Zero-mean sequences imply E[f(x, y)] = 0, E[g(x, y)] = 0 and E[f(x, y)] = 0. Similarly, stationary sequences can be defined in terms of correlation as under: E[ƒ (x, y).ƒ (i, j)]=rf ( x − i, y − 1) | E[g (x, y).g (i, j)] = rgg (x-i, y-j) f 88 → Auto correlation Elf (x, y). g(i, j)] = g(x-i, yj) → cross correlation The zero mean image model is given by the following expression. List the major drawbacks of Wieners filter.
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As a matter of fact, the Wiener filter is most popular filter and is used for restoration. The main limitation of the earlier discussed methods viz., Inverse filtering and Pseudo-Inverse filtering is that they are sensitive to noise (The Wiener filter exploits the statistical properties of the image and can be used to restore images in the presence of blur as well as noise.
Let f(x, y), g(x, y) and f(x, y) be zero mean random sequences.
Zero-mean sequences imply E[f(x, y)] = 0, E[g(x, y)] = 0 and E[f(x, y)] = 0. Similarly, stationary sequences can be defined in terms of correlation as under:
E[ƒ (x, y).ƒ (i, j)]=rf ( x − i, y − 1) |
E[g (x, y).g (i, j)] = rgg (x-i, y-j) f 88
→ Auto correlation
Elf (x, y). g(i, j)] = g(x-i, yj) → cross correlation The zero mean image model is given by the following expression. List the major drawbacks of Wieners filter.
![Zero-mean sequences imply Elf(x, y)] = 0, E[g(x, y)] = 0 and E[f(x, y)] = 0.
%3D
Similarly, stationary sequences can be defined in terms of correlation as under:
E[f (x, y).f (i, j)]= rg (x-i,y-j)]
E[g (x, y).g (i, j)] =rg (x - i, y- j)
→ Auto correlation
...(4.14)
Elf (x, y) · 8(i, i = r(x - i, y - j) → cross correlation
The zero mean image model is given by the following expression:
%3D
g(x, y) = E£'p (i, j). f (x = i, y- j)
...(4.15)
Let us redraw figure 4.1. Here, the noise term, n(x y), is ignored
Degradation
function
Restoration
function
ha(x.y)
7(x,y)
f(x,y) -
g(x.y)
hp(x,y)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F654d3a95-bae4-4bae-b275-2cead31ec48c%2Fdd01c58e-7333-4b43-b09c-d5c0ba877d09%2F3pmo9e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Zero-mean sequences imply Elf(x, y)] = 0, E[g(x, y)] = 0 and E[f(x, y)] = 0.
%3D
Similarly, stationary sequences can be defined in terms of correlation as under:
E[f (x, y).f (i, j)]= rg (x-i,y-j)]
E[g (x, y).g (i, j)] =rg (x - i, y- j)
→ Auto correlation
...(4.14)
Elf (x, y) · 8(i, i = r(x - i, y - j) → cross correlation
The zero mean image model is given by the following expression:
%3D
g(x, y) = E£'p (i, j). f (x = i, y- j)
...(4.15)
Let us redraw figure 4.1. Here, the noise term, n(x y), is ignored
Degradation
function
Restoration
function
ha(x.y)
7(x,y)
f(x,y) -
g(x.y)
hp(x,y)
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