Title:
Image Denoising in the Wavelet Domain using Wiener Filtering

Team Members:
Nevine Jacob and Aline Martin 

Problem statement and proposed approach:

Wavelet transforms have become a very powerful tool for denoising an
image.  One of the most popular method consists of thresholding the
wavelet coefficients (using the hard threshold or soft threshold).  In
this paper, we perform Wiener filtering on the wavelet coefficients to
denoise the image. 

We propose to denoise a degraded image X given by X = S + W, where S is
the original image and W is an Additive White Gaussian noise with
unknown variance.  The first step involves applying the Haar Wavelet
Transform to the noisy image X.  Adaptive Wiener filtering is then
performed on the wavelet coefficients.  The final step involves applying
the inverse Haar wavelet transform on the denoised wavelet coefficients. 
The results of this method are compared with those obtained by other
well-known methods such as Soft and Hard Thresholding in the wavelet
domain; Global, Local and Iterative Wiener Filtering in the Fourier
domain.  The criteria used for comparison in these methods are the
Visual Quality and Mean Square Error. 


References:

Image Denoising via Wavelet-Domain Spatially Adaptive FIR Wiener Filtering
Zhang, H.; Nosratinia, A.; Wells, R.O., Jr.;
Acoustics, Speech, and Signal Processing, 2000.  ICASSP '00. 
Proceedings.  2000 IEEE International Conference on, Volume: 6, 5-9 June
2000 Pages: 2179 - 2182 vol.4

Denoising via block Wiener filtering in wavelet domain
Strela, V.
Proc. Third European Congress of Mathematics,
Progress in Mathematics series, Birkhauser Verlag, Barcelona (2000)

Wavelet domain image denoising by thresholding and Wiener filtering
Kazubek, M.
Signal Processing Letters, IEEE, Volume: 10, Issue: 11, Nov. 2003
265 Vol.3

De-noising by Soft-Thresholding
David L. Donoho
IEEE Transactions on Information Theory, Vol. 41, No. 3, May 1995
Image Denoising using Wavelet Thresholding and Model Selection
Shi Zhong
Image Processing, 2000, Proceedings, 2000 International Conference on,
Volume: 3, 10-13 Sept.  2000 Pages: 262