Questions About 'trous' Denoising Plugin

[McAuley, Grant (LLU)]

I want to understand how to use the 'trous wavelet filter' plugin.  I think I have at least a pretty good *intuitive* understanding about the basics of wavelets, and would welcome any information about this at that level.

Am I correct:

1) The filtering is based on the 'cascading filter' idea
2) k1 is the coefficient that corresponds to the highest detail component of the image
3) k5 is the coefficient that corresponds to the lowest detail (most course) component of the image


Re the coefficient values:

3) if I set k1 = '5.0', what does this mean?  Does it mean 'remove the image components if the k1 coef of the wavelet transform is below 5.0'?  Is it a threshold in another sense?  

Finally, if someone could recommend an easy reading reference on this that would be helpful as well.

[Olivier Marchal]

Hello,
in order ot filter the image, we apply a wavelet transform that produces a
serie of 5 other images. Each new image represents a scale in the wavelet
space. The first scale corresponds to the lowest component details and the
fifth to the highest details. In other words, the noise, which is associated
to little structures, is generally found in the scales 1 and 2.

To remove the noise we used an algorithm developed by Fionn Murtagh and a
thresholding function on each coefficient at each scale. We estimate that a
coefficient is associated to noise if :
abs(coeff) < k_i*S*dev_s_i
where :
coeff   =  the value of the coefficient
S       =  standard deviation of the noise in the original image
dev_s_i =  standard deviation of the noise in the scale i
k_i     =  thresholding factor at scale i
In order to threshold small details, you have to modify the values of k1 and
k2. A value of 4 for k1 and 3 for k2 are sufficient most of the time. If the
image is very noisy, you can take a higher value for k1 and k2.
Olivier