# Noise characterization of wavelet coefficients

Started by June 29, 2004
```Hi,

I hope this question about wavelets is not too far off topic in this
forum...

I have some image data with noise for which the noise statistics (mean,
variance) are known :

noisy image = true image + noise in image domain

In my case, the mean and variance is not constant over the image (correlated
noise).

When I perform a wavelet transform on this noisy image, I presume I can
treat the "noisy" wavelet coefficients as:

noisy coefficients = true coefficients + noise in wavelet domain

My question is - How can I find the statistical properties of the "noise in
wavelet domain" term? This may be a naive question, or very
complicated...I'm not sure. Any references about where I might start looking
would be appreciated.

Specifically, I am using the discrete dyadic wavelet transform
(non-subsampled).

Many thanks,
Geoff

```
```"g" <noreply@noreply.com> wrote in message
news:<cPkEc.610098\$Ar.130800@twister01.bloor.is.net.cable.rogers.com>...
> Hi,
>
> I hope this question about wavelets is not too far off topic in this
> forum...
>
> I have some image data with noise for which the noise statistics (mean,
> variance) are known :
>
> noisy image = true image + noise in image domain
>
> In my case, the mean and variance is not constant over the image (correlated
> noise).

The above is a pretty basic signal model, even though some details are
not clear. What do you mean by "correlated noise"? That the noise
correlates with the signal or that the noise autocovariance is a
2D Delta? Do you know the numerical values for variance and mean for
the noise over the image, or do you only know that the noise have these
general properties?

> When I perform a wavelet transform on this noisy image, I presume I can
> treat the "noisy" wavelet coefficients as:
>
> noisy coefficients = true coefficients + noise in wavelet domain
>
> My question is - How can I find the statistical properties of the "noise in
> wavelet domain" term? This may be a naive question, or very
> complicated...I'm not sure. Any references about where I might start looking
> would be appreciated.
>
> Specifically, I am using the discrete dyadic wavelet transform
> (non-subsampled).

I don't know much about wavelets, but the problem statement seems to
be the same as the basis for Wiener filters. Wiener filters require
that the statistical properties of the noise is uncorrelated with the
signal and the noise spectrum is known (or rather, assumed) a priori.

You may want to ask for help on such problems in sci.image.processing.

Rune
```