Image Denoising in the Wavelet Domain Using Wiener Filtering Nevine Jacob – Aline Martin ECE 533 Project – Fall 2004 nmjacob@wisc.edu – alinemartin@wisc.edu

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

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

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

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

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

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

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