# Pixel density - can the playing field be leveled???

Started Jun 6, 2009 | Discussions thread
Re: Noise filters...

John1940 wrote:

Emil, I might have missed information on "better noise filters." How
do they reduce noise and yet not detail?

As an example, Noise Ninja uses wavelet methods according to the spiel on their website. Of course the precise version of their algorithm is proprietary, but a common NR method in the image processing literature is called "wavelet shrinkage".

For example, a simple wavelet filter splits the image into its 2x2 binned version, together with a set of differences between the binned version and the original. One can always get the original back by summing the binned image and the residual differences. One can then repeat this binning several times. This gives a representation of the image on successively coarser scales; the amplitudes of the various residual differences on this hierarchy of scales are called the "wavelet coefficients".

The heart of the NR is then to give a criterion for how much of the wavelet coefficient amplitudes are due to noise; then those coefficient amplitudes are shrunk, and the image is put back together. The result is a deniosed image.

Does detail in the image stand
out in a detectable way from the noise due to a lack of randomness?
--

Yes, an image feature is coherent across several pixels and if one can detect the correlation of pixel values above the random fluctuations of the noise then one can remove much of the noise leaving the feature relatively intact. It's similar to the way binning pixels reduces noise, in the example above indeed binning is part of the wavelet transform. For instance, if there is a horizontal edge and you bin in the horizontal direction, the edge sharpness is retained but the horizontal fluctuations are reduced.

The residuals carry the fine detail that is lost in the binning, and the trick is to figure out what fraction of those residuals is noise. Typically when the coefficients are large there is some noise present, and so shrinking the coefficient down (not necessarily to zero) gets rid of noise and leaves some of the detail. The threshold for when the wavelet coefficient is shrunk is determined adaptively based on the image content, and that is where the detail retention is (hopefully) optimized.

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