Author Topic: -log(SNR) does it make any difference?  (Read 2006 times)

Offline bulo4kin

  • Newcomer
  • Posts: 6
    • View Profile
-log(SNR) does it make any difference?
« on: 2013 April 04 05:43:54 »
Dear All,

please, let me know if you know what happens to Signal to Noise ratio (SNR) of an image after we take    -log(SNR)?
What happens to Signal and Noise components (please, formulas)?

Thanks!
« Last Edit: 2013 April 04 05:56:18 by bulo4kin »

Offline Carlos Milovic

  • PTeam Member
  • PixInsight Jedi Master
  • ******
  • Posts: 2173
  • Join the dark side... we have cookies
    • View Profile
    • http://www.astrophoto.cl
Re: -log(SNR) does it make any difference?
« Reply #1 on: 2013 April 04 06:10:06 »
= log(noise) - log(signal)
Regards,

Carlos Milovic F.
--------------------------------
PixInsight Project Developer
http://www.pixinsight.com

Offline bulo4kin

  • Newcomer
  • Posts: 6
    • View Profile
Re: -log(SNR) does it make any difference?
« Reply #2 on: 2013 April 04 06:15:05 »
= log(noise) - log(signal)


sorry just to make sure, please, mind the minus "-"

 log(S/N)=log(S)-Log(N)

 -log(S/N)=log(N)-Log(S)

Correct? To be frank I am surprised because I though that there is more to that than just simple math...I just checked that and apparently the formula is not correct because it results in negative S/N????

Also, what about the final Signal and Noise (two images) when log(S1/N1)+log(S2/N2) and log(S1/N1)-log(S2/N2)?

Thanks a lot!
« Last Edit: 2013 April 04 09:24:47 by bulo4kin »

Offline bulo4kin

  • Newcomer
  • Posts: 6
    • View Profile
Re: -log(SNR) does it make any difference?
« Reply #3 on: 2013 April 04 11:18:56 »
lol, it is getting very interesting...

Newberry, "Signal-to-noise considerations for sky-subtracted CCD data", Publications of the Astronomical Society of the Pacific 103:122-130, Jan 1991

from the paper above I finally managed to figure out how to calculate SNR after any math operation.
Let's try to take -log(image)

S1/N1 - old signal/noise, S/N - new signal/noise

S=-logS1
differential dS=d(-logS1)=-dS1/(S1*ln10), where dS=N and dS1=N1

S/N=logS1*ln10*(S1/N1) but wait that means that if one takes -log(image) one actually increases S/N! Is that really possible?
I thought that no matter what we do to an image (subtraction, normalization) we always reduce S/N?

Please, correct me if I am mistaken.

Offline Geoff

  • PixInsight Padawan
  • ****
  • Posts: 887
    • View Profile
Re: -log(SNR) does it make any difference?
« Reply #4 on: 2013 April 04 15:26:22 »

I thought that no matter what we do to an image (subtraction, normalization) we always reduce S/N?

Please, correct me if I am mistaken.
When you combine two frames by either addition or subtraction, the noise increases as sqrt(n1^2 + n2^2), but this tells you nothing about the signal to noise ratio. If you were to  take two images of the same object and add them, then the signal to noise ratio would increase. (That's why we stack light frames.) On the other hand, if you subtract them, you still have the same amount of noise, but (virtually) no signal, so the signal to noise ratio goes down to zero.  Dark subtraction, flat division etc is a whole new story.
Geoff
« Last Edit: 2013 April 04 21:17:09 by Geoff »
Don't panic! (Douglas Adams)
Astrobin page at http://www.astrobin.com/users/Geoff/
Webpage (under construction) http://geoffsastro.smugmug.com/