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Image Denoising in the Wavelet Domain Using Wiener Filtering

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

  2. = + Problem statement Y = X + W Goal: recover X from Y 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 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 Level 1 – Wiener Filtered coefficients Noisy Im Denoised Im Image Denoising in the Wavelet Domain using Wiener Filtering

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

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

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

  7. Simulation Results • MSE Image Denoising in the Wavelet Domain using Wiener Filtering

  8. 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 Image Denoising in the Wavelet Domain using Wiener Filtering