Image Denoising
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Transcript of Image Denoising
Submitted by, APOORVA PRAKASH H S(1SI09EC118)
Under the guidance of,Dr. K.V. Suresh, M.Tech, Ph.D.,Professor and HeadDepartment of E&CSIT, Tumkur
Image denoising in the wavelet domain using Wiener filtering
DEPARTMENT OF ELECTRONICS AND COMMUNICATION, 2012-2013
Technical Seminar on
Outline
IntroductionLocal Wiener filteringDoubly local Wiener filteringExperimental resultsConclusionReferences
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Why do we want to denoise
Visually unpleasantBad for compressionBad for analysis
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Introduction
Image denoising means removing unwanted noise in order to restore the original image
Wavelet transform provides us with one of the best methods for image denoising
Squared window
Elliptical directional window to improve further denoising performance
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Problem statementY = X + W
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= +
Y: Noisy image X: Original image W: White Gaussian noise
Assumptions • X is unknown• X and W are uncorrelated• Noise variance may be unknown
Goal: recover X from Y
Noise removal techniques
Linear filteringNon linear filtering Recall
H[ai fi(x) +aj fj(x) = ai H[fi(x)] + aj H[fj(x)]
= ai gi(x) +aj gj(x)
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SystemH
f(x) g(x)
Local Wiener filtering
1) Original Barbara image2) Horizontal subband3) Vertical subband4) Diagonal subband
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1 2 3 4
Figure 1: Three undecimated oriented subbands in the third level for the image “Barbara” [3]
Local Wiener filtering(contd.)
A longer elliptic window is used for horizontal subband
A higher elliptic window is used for vertical subband
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(1)
Local Wiener filtering(contd.)
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The local wiener filtering in the wavelet domain includes two important steps;
• Signal variance estimation
• Signal wavelet coefficient estimation
(2)
Local Wiener filtering(contd.)
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The signal variance of each noisy wavelet coefficient is estimated by the local average
The signal wavelet coefficients are estimated by the Wiener filtering
(3)
(4)
Doubly local Weiner filtering
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Figure 2: Flow diagram of the DLWFDW in the wavelet domain [3]
Doubly local Weiner filtering(contd.)
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The total error in each subband is written as
Selecting a too large or too small window is not a good choice
(5)
Primary guides about size selection
For the decimated case, the optimal sizes of the windows that minimize the total error should be gradually reduced
For the undecimated case, the optimal sizes of the windows should be gradually increased with scales
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How to select wavelet pairs
In the first LWFDW, wavelet bases of short support are often used as the DWT1 or SWT1
In the second LWFDW, wavelet bases of high vanishing moments are often used as the DWT2 or SWT2
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Experimental results
σ 10 15 20 25
D3+D4 33.05 30.66 29.07 27.86
D4+S8 33.24 30.85 29.27 28.07
D3+S8 33.16 30.81 29.26 28.08
S8+S8 33.02 30.71 29.16 28.01
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Table 1: comparison of different wavelet pairs [3]
Experimental results(contd.)
r 5 6 7 8 9
a=1 31.61 31.99 32.07 32.10 32.07
a=2 32.03 32.15 32.20 32.19 32.15
a=3 32.10 32.19 32.19 32.13 32.08
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Table 2: comparison of different windows [3]
Conclusion
Doubly Local Wiener Filtering algorithm is an efficient, fast approach and low complexity
The algorithm outperforms the relevant algorithms using the 2-D separable wavelets
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References[1] M. K. Mihcak, I. Kozinsev, K. Ramchandran, and P.
Moulin, “Low-complexity image denoising based on statistical modeling of wavelet coefficients,” IEEE Signal Process. Lett., vol. 7, no. 6, pp. 300–303, Jun. 1999.
[2] S.P.Ghael, A.M.Sayeed and R.G.Baraniuk,
“Improved wavelet denoising via empirical Wiener filtering” in Proc. SPIE, vol. V, San Diego, CA, pp. 389–399, July 1997.
[3] Peng-Lang shui, “Image denoising algorithm via doubly local wiener filtering” Lett., vol. 12, no. 10, pp. 681-684, Oct 2005
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Thank you
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