Title: Nonlinear Denoising Techniques

Name: Jungwon Lee

E-mail: jungwon@leland.stanford.edu

Goals and Work to be carried out:
 There are many nonlinear methods for noise reduction such as the one 
using wavelet transform, using median filters, and using inhomogeneous 
diffusion filtering algorithm.  Among those methods, I'll choose the 
Bayesian denoising technique in the wavelet domain and the technique 
using tri-state median filter.
 The Bayesian denoising algorithm using wavelet transform seems to work 
very well compared to other methods. Of course, it is better than the 
optimal linear filter, Wiener filter, since the Bayesian denoising 
algorithm exploits the higher order statistics than Wiener filter which 
uses only first and second order moment.
 A novel nonlinear filter called tri-state median filter was proposed 
last December. A tri-state median (TSM) filter incorporates the standard 
median (SM) filter and the center weighted median (CWM) filter into an 
impulse noise detection framework to determine whether a pixel is 
corrupted, before applying filtering unconditionally. With proper 
selection of threshold, it outperforms the SM filter and CWM filter.
 The Bayesian denoising algorithm works well for the additive white 
Gaussian noise and the tri-state median filter is good for impulse 
noise, which corrupts digital images during the acquisition or transmission 
through communication channels. Since the types of the noise that two 
algorithms tries to eliminate are different, they are difficult to be 
compared with each other directly. However, I'll compare these two algorithms 
using two types of the noise, and confirm that Bayesian denoising algorithm 
is better than the TSM filter technique for the additive white Gaussian 
noise and vice versa for the impulsive noise. Moreover, I'll compare the 
Bayesian denoising algorithm with Wiener filtering and the TSM filter 
technique with the SM filter and CWM filter.
 Although I guess that 40-50 hours are not enough for improving one of the 
techniques, I'll try to improve one of the techniques if time permits.

Reference:
E. P. Simoncelli and E. H. Anderson. Noise removal via Bayesian wavelet 
coring. Proceedings of the 3rd IEEE International Conference on Image 
Processing, Vol. I, pp. 379-382, 1996.

E P Simoncelli. Bayesian Denoising of Visual Images in the Wavelet Domain 
In Bayesian Inference in Wavelet Based Models. eds. P Muller and B Vidakovic.
 Chapter 18, pp 291-308. Springer-Verlag, Lecture Notes in Statistics 141, 
1999.

Tao Chen, Kai-Kuang Ma, Li-Hui Chen. Tri-state median filter for image 
denoising. IEEE Transactios on Image Processing, Vol. 8 12, Dec. 1999, 
pp 1834-1838.


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Name : Jungwon Lee
E-mail : jungwon@leland.stanford.edu
Homepage : http://www.stanford.edu/~jungwon
Address : 19C Escondido Village, Stanford, CA 94305, U.S.A.
Phone / Fax : 1-650-497-3551
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