1. Image Denoising in the Wavelet Domain Using Wiener Filtering
Nevine Jacob – Aline Martin
ECE 533 Project – Fall 2004 –

2. Image Denoising in the Wavelet Domain using Wiener Filtering
Problem statement
Y = X + W = +
W: White Gaussian noise
Y: Noisy image
X: Original image
Assumptions
1/ X is unknown
2/ X and W are uncorrelated
3/ noise variance may be unknown
Goal: recover X from Y
12/14/2004
Image Denoising in the Wavelet Domain using Wiener Filtering

3. Wiener Filter in the Wavelet domain
3 steps:
1/ wavelet transform
2/ Wiener Filter on the wavelet coefficients
3/ Inverse wavelet transform WF
Level 1
Noisy Im
Level 1 – Wiener Filtered coefficients
Denoised Im
12/14/2004
Image Denoising in the Wavelet Domain using Wiener Filtering

4. Wiener Filter in the Wavelet domain
Level 1
Level 1 – Wiener Filtered coefficients
: variance of the noise
12/14/2004
Image Denoising in the Wavelet Domain using Wiener Filtering

5. Image Denoising in the Wavelet Domain using Wiener Filtering
Simulation Results
Wavelet domain: WF vs Thresholding
Wiener Filter wavelet domain
Soft Thresholding
Hard Thresholding
MSE = 110
MSE = 140
MSE = 175
12/14/2004
Image Denoising in the Wavelet Domain using Wiener Filtering

6. Image Denoising in the Wavelet Domain using Wiener Filtering
Simulation Results
WF: wavelet domain vs Fourier Domain
Wiener Filter wavelet domain
Global Wiener Filter
Local Wiener Filter
MSE = 75
MSE = 110
MSE = 115
12/14/2004
Image Denoising in the Wavelet Domain using Wiener Filtering

7. Image Denoising in the Wavelet Domain using Wiener Filtering
Simulation Results
MSE
12/14/2004
Image Denoising in the Wavelet Domain using Wiener Filtering

8. Image Denoising in the Wavelet Domain using Wiener Filtering
Conclusion
Wiener Filter in the Wavelet domain performs better than thresholding methods and Wiener Filter in the Fourier Domain
Improve denoising along the edges
Need for a better quantitative criteria
12/14/2004
Image Denoising in the Wavelet Domain using Wiener Filtering