Noise Reduction in the Wavelet Domain

1
Noise Reduction in theWavelet Domain

• EE368A Digital Image Processing
• Spring 2001
• Shahriyar Matloub Augusto Román

2
Outline

• Wavelet Decomposition

• Denoising in Wavelet Domain

• Bayesian Estimation
• Parameterized Model
• Noise Power Compensation
• Estimator Functions

• Results

• Conclusion

3
Wavelet Decomposition
Image
4
Denoising in Wavelet Domain
Noisy Image
?
5
Threshold Methods

• Hard
• Eliminate less-significant coefficients.
• Optimal threshold has been determined by Donoho
  and Johnson (93)
• Soft
• Shrink less-significant coefficients more than
  significant coefficients
• Bayesian Estimation by Simoncelli (96)

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Bayesian Estimation

• Best MSE estimator needs PDF of original image
  and PDF of noise.

• Assumption of a Gaussian distribution for noise.

?

• Assumption of a Gaussian distribution for
  magnitude of coefficients of natural images.

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Bayesian Estimation, cont.

• It seems that the magnitude of coefficients for
  natural images have approximately Laplacian
  distributions.

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Noise Power Compensation

• With large noise power, Maximum Likelihood
  estimation does not provide a good estimate for
  noise power.

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Noise Power Compensation

• We developed subband-adaptive compensation
  functions to increase estimated noise.

• a - constantD - total of subbandsd -
  current subband leveln - order of function

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Estimator Functions
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Results
B
A
C
D
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Conclusions

• Compensation functions has improved performance
  of the algorithm.
• Future work
• Deriving an adaptive algorithm for the function
  parameters based on noise power.
• Investigating other estimation schemes to find
  the estimated distribution parameters.