SNR estimation - StdDev vs. AvgDev in Statistics Process

[SkyAnd]

Hi everyone, hope that someone can help me with my SNR and Statistics (Process) issues....

I use an QHY 268-C OSC with Astronomik L2 UV/IR Cut Filter on a APM 140/980 (f7) refractor. A bortle 4 sky is typical in my backyard , fairly good conditions for an astro photographer. PixInsight is my main stacking and post processing software and I use it for nearly 6 month.

I tried to find out a lttle bit more about the SNR results of my pictures, using the Statistic process and simply dividing the MEAN by the StdDev. I was very surprised, when I recognized, that the value of StdDev doesn´t change threw the calibration and stacking process - for that reason the calc. SNR is bad.

See the following example with 300 sec (M92) - DSO Mode, Gain 26, Offset 50, Chip Temp -10°C - RAW single frame left, CAL single frame in the middle (MasterDark with app. Mean = 850 ADU), and INT stack on the left side (only 13x 300 sec = 65 min) RGB->Grey

The StdDev never changed, but the AvgDev and the MAD decreases in the process - is AvgDev the figure I have to use instead of StdDev (what is the difference?) to get a better assumption for SNR = MEAN/AvgDev?

Using the SNR script of Hartmut Bornemann, the results are not so bad and get better and better threw the process - is this the better way to have a realistic comparison? Here are the figures:

Thanks a lot for your help
CS Andreas

 

[bulrichl]

Hi Andreas,

the mean value of a light frame that is shown in the Statistics process is dominated by the mean background of the image. During image calibration the MasterDark is subtracted. So it doesn't make any sense to compare mean(RAW)/stddev(RAW) with mean(CAL)/stddev(CAL). The change of this ratio is mainly caused by subtraction of the mean value of the MasterDark (in your case about 850 ADU on the average). The change of this ratio has no bearing on SNR. I tried to explain that to you in Astronomie.de already. Sorry if I expressed myself unclearly.

Bernd

 

[SkyAnd]

Hi Bernd (and all others),

I´m sorry, but I think there is a misunderstandig in my question here in comparison to my first post in Astronomie.de (German forum)

I´ve added there the same question as here after your reply (Bernd), but get no answer till now. Your answer above is absolutely acceptable for my first question in the German Forum. If you like we can communicate there again in German to avoid bad interpretations.

The main question here is (1. picture): Why the StdDev doens´t change from calibrated single-frame (CAL) to the stacked image (INT)? It has to become a better result because of the stacking - better signal and a noise only growing by square root of signal - Second: is the AvgDev the better assumption for noise instead of StdDev (Process Statistics in PI), because in the example its decreasing threw stacking and StdDev does not?

And the last question here is (2. picture): is the SNR script of Hartmut Bornemann the best choice to find out about the SNR in an image, or is it to unprecised?

That´s all
Thank you for helping me clear skies
Andreas

 

[bulrichl]

I append histograms and statistics of one calibrated image and the integration of a project of 52 images of M 94.

When comparing different frames which were captured under similar conditions, the signal doesn't change much. By integrating many frames the noise is greatly diminished, this is obvious from the width of the background peak in the histogram, but it is not reflected by the stdDev of the whole image:

               R        G        B
calibrated     416      398      379
integration    503      411      464

This changes drastically when you create a preview of a region containing pure background and compare the stdDev of the previews:

               R        G        B
calibrated     38.6     27.1     32.5
integration    4.9      3.5      4.1

So by integrating 52 frames, the noise in the background was decreased by 87 %. This will bear on SNR.


Bernd

 

[bulrichl]

Additional comment:

MAD and AvgDev respectively are robust measures of dispersion in descriptive statistics (robust = resilient to outliers). You can find here how they are calculated:

MAD = Median absolute deviation, e.g.: https://docs.tibco.com/pub/sfire-an...Guide/stat/stat_median_absolute_deviation.htm

AvgDev = Average absolute deviation: e.g.: https://en.wikipedia.org/wiki/Average_absolute_deviation

The Intensity values in a linear astro image strongly deviate from a normal distribution. The value of the stdDev of a whole image is not a good measure of dispersion, because stdDev is not robust. In this thread I tried to illustrate this with histograms und results of the Statistics tool: for a whole image and for a preview which contains exclusively background. For the previews, the values of stdDev, MAD and AvgDev are nearly identical.

Bernd

 

[SkyAnd]

Thanks a lot Bernd , that´s very helpful - can you please do an additional statement to the Script "SNR" of Hartmut Bornemann?

CS
Andreas

 

[bulrichl]

I executed the SNR script on the (calibrated, cosmetically corrected and debayered) subframe and the integration result shown above in post #4:

_2022_05_27_0050_c_cc_d
Calculating SNR
* Channel #0
SNR = 4.956e+02, 26.95 db 
* Channel #1
SNR = 3.671e+02, 25.65 db 
* Channel #2
SNR = 3.381e+02, 25.29 db 

masterLight_BIN_1_6248x4176_EXPOSURE_300_00s_FILTER_NoFilter_RGB_integration
Calculating SNR
* Channel #0
SNR = 2.508e+04, 43.99 db 
* Channel #1
SNR = 2.053e+04, 43.12 db 
* Channel #2
SNR = 1.971e+04, 42.95 db

The ratio of the SNR values (integration/subframe) should give the SNR gain:

Ch    gain
0    25080/496 = 50.6
1    20530/367 = 55.9
2    19710/338 = 58.3

This result is to good to be true: The theoretical upper limit of SNR gain is sqrt( n ), where n is the number of subframes. I processed 52 frames, so the theoretical upper limit of SNR gain is sqrt(52) = 7.8.

Bernd