Saturn

[Mike]

Noise can also be used to describe other artifacts, including diffraction spikes ......

Oh god no! Not again !

[Carole]

Thanks Ian and John, will take a look at the website John suggested.  I have been trying to remember back to that talk Mike gave on Astro-Imaging at the members evening some time ago, and remember him talking about noise, but came away with a different impression of what it was. 

Mike any chance of a repeat performance?

A bit more leant.

Carole

[Rocket Pooch]

John,

Frodo has waveletts in his hair, thats about as much as I'm going to explain.

Chris

[MarkS]

Fay - Could you explain wavelets for me please 

Explaining wavelets - how to do this intuitively - now there's a challenge.  Maybe this should be in a new thread ...

Here's my attempt.

Wavelets allow you to increase definition and contrast in the final image when the original image has been degraded by:
1) Slight Gaussian blur due to atmospheric conditions
2) Slight defocus in the optical train
3) Central obstruction in the optics (e.g. using an SCT instead of a refractor)

It does this by allowing amplitude adjustments (amplification) of frequency components in the image. It is very analagous to using the equalisation controls of some household audio amplifiers - you can boost low, mid or high frequencies independently.

But why does boosting some frequencies improve the image?  The reason is that the three blurring effects mentioned above do so by attenuating certain frequencies in the frequency band.  Wavelets boost those frequencies back to where they should be.  Watching the universe through the atmosphere is a bit like recording a concert from behind a pair of curtains - you'll end up with a muffled recording.  But if you play back the recording with the correct settings on the equaliser then you can make it sound more natural again.  This is exactly what wavelets is doing to your prized image: the sliders in the wavelet application are behaving just like the sliders on your audio equaliser.

There is a fly in the ointment however - noise.  Your degraded image will incorporate the same amount of noise as an undegraded image.  So when you boost some frequencies you are also boosting the noise associated with those frequencies.  This ends up causing speckely/blobby effects right across your final image.  Going back to the audio analogy, when you boost certain frequency bands using your equaliser you end up increasing the backgound hiss through the speakers.  And this is where things become very subjective: just as various people can live with varying amounts of hiss as they play back their degraded audio recordings, so various people can live with various amounts of speckly/blobby noise in their final image.  There is no right or wrong here - improving definition and contrast will also increase the speckly/blobby noise  - each person makes their own compromise between the two.

Now, if your degraded image has low levels of noise then the frequencies can be boosted much higher before noise starts to become objectionable.  This is why we stack hundreds of frames of Saturn together - it improves the ratio of the signal that we want versus the noise that we don't want.

In theory you can also apply wavelet transforms to improve definition in your images of faint galaxies.  But generally speaking the signal to noise ratio of these images is much lower and you cannot boost the frequencies very far before the speckly/blobby effects become severe.

For the more technically minded amongst you, there is a good reason why it is very important that your focusing is as accurate as possible.  Wavelets can reverse mild amounts of defocusing but for more severe cases a defocused image, for certain frequencies,  contains phase reversals as well as attenuation.  These phase reversals can only be corrected by a more sophisticated technique - deconvolution.  There are whole families of these deconvolution techniques - Wiener, Richardson-Lucy (famous for the old Hubble images), Maximum Entropy to name but a few.  But now we are well outside the scope(!) of an intuitive explanation.

[Rocket Pooch]

sounds like decon to me ?

[MarkS]

Wavelets is definitely deconvolution.  I should've made that clearer.

[Fay]

No wonder John asked me to explain wavelets!!
I'm glad Mark took up the challenge, very well, before I could post the same answer!