How to calculate detection limit for a map

[Ben Buse]

Hi,

Using the formula for detection limit we can easily calculate the detection limit for a single pixel. But this is not the "real" detection limit in the sense that we can often see features on a map which have a lower concentration. This is particularly the case when you have a lot of pixels in the image with the dwell time for each individual pixel quite short. So that your eye blurs the pixels and picks out the features - whereas the error and detection limit for each of the noisy pixels is high.

I image it's a question related to signal-noise ratio and determining a feature from noise - for the larger the feature the easier it is to determine from the background noise.

In terms of calculating the detection limit can we just calculate it based on 4 pixels or 9 pixels. With the detection limit of a feature being a function of the number of pixels within the feature. I.e. to calculate detection limit of a feature could you multiple the counts and the count time by the number of pixels within the feature.

Thanks

Ben

[John Donovan]

Hi,

Using the formula for detection limit we can easily calculate the detection limit for a single pixel. But this is not the "real" detection limit in the sense that we can often see features on a map which have a lower concentration. This is particularly the case when you have a lot of pixels in the image with the dwell time for each individual pixel quite short. So that your eye blurs the pixels and picks out the features - whereas the error and detection limit for each of the noisy pixels is high.

I image it's a question related to signal-noise ratio and determining a feature from noise - for the larger the feature the easier it is to determine from the background noise.

In terms of calculating the detection limit can we just calculate it based on 4 pixels or 9 pixels. With the detection limit of a feature being a function of the number of pixels within the feature. I.e. to calculate detection limit of a feature could you multiple the counts and the count time by the number of pixels within the feature.

Thanks

Ben

Hi Ben,
You are absolutely correct about the human eye's ability to average pixels and see patterns in noisy images-  in fact our eyes/brain are often too good and we see patterns that aren't actually there!

But yes, this is absolutely something that can be done and I would be pleased to implement it in CalcImage as soon as I get a chance. 

I finally(!) finished converting all the old graphics calls in PFE so maybe I will have a bit more time now for things like this.  Feel free to discuss here what features you would like to see regarding this detection limit processing. Perhaps it could go into the RGB/image math window as a third option?
john

[Ben Buse]

That be good to think about implementing something. I suppose my question is though first is this a valid approach to describe the "real" detection limit or does anyone know of any better statistical equations or approaches to deal with the problem

Thanks

Ben

[Probeman]

That be good to think about implementing something. I suppose my question is though first is this a valid approach to describe the "real" detection limit or does anyone know of any better statistical equations or approaches to deal with the problem

Hi Ben,
I think a pixel clustering method as you suggest above should work just fine.  After all, counting statistics are based solely on the total number of photons.  In fact one could simply "bin" the image to produce a file, which would then be much more amenable to statistical tests.

In fact, if one "binned" the raw image files (for example, the raw intensity .grd files), the statistics would propagate through the CalcImage map quantification calculations quite naturally...

[jon_wade]

The ability to see patterns in random data is known as Apophenia.  Its what sets us apart from animals - on the other hand, scepticism of such patterns sets us apart from palaeontologists!   ( I don't *really* mean that, honest!)

umm...In the back of my mind a thought stirs which may or may not be right.  This sounds like a form of median filter?

if so, will this actually produce a meaningful detection limit calculation for those binned areas _ i mean, it may potentially produce a better image (which is all that matters), but you'd have to propagate the peak/background in some meaningful way, no? 

[Probeman]

The ability to see patterns in random data is known as Apophenia.  Its what sets us apart from animals - on the other hand, scepticism of such patterns sets us apart from palaeontologists!   ( I don't *really* mean that, honest!)

Hi Jon,
That is so true.  In fact humans are even more adept at seeing faces in noise. If you see Elvis in peeling paint, this is probably "pareidolia" and is illustrated in the PPT slides attached below, which I used for years in my "Weird Science" freshmen seminar. Here's a famous example:

https://en.wikipedia.org/wiki/Chonosuke_Okamura

if so, will this actually produce a meaningful detection limit calculation for those binned areas _ i mean, it may potentially produce a better image (which is all that matters), but you'd have to propagate the peak/background in some meaningful way, no?

This is essentially what I was trying to get across to Ben above.

If one bins the raw data images before loading them in CalcImage (that is on and off-peak x-ray maps) using a 2 x 2 bin, each pixel will now be approximately 4 times the intensity and hence about twice the sensitivity- but with lower resolution of course.  In this case the binned pixels will propagate the improved statistics quite naturally through the quant calculations.

However, if one really wants to improve detection limits for x-ray mapping, one can also utilize MAN background corrections.  With this method we can improve sensitivity by roughly 40% and in approximately 1/2 the acquisition time as described here:

http://probesoftware.com/smf/index.php?topic=425.msg2296#msg2296

It won't work for all samples, but it can work for pure elements, oxides, simple silicates and sulfides.  That is, it probably won't work for monazite, but will work for SiO2, TiO2, ZrSiO4, FeS2, etc.  Any matrix that one can obtain a "blank" standard for to maintain accuracy.

[Jeremy Wykes]

Would there be any utility in implementing a spatial autocorrelation algorithm like Moran's I, or Geary's C?

Geary's C might be more useful as you can move a sampling window over the image to see examine the correlation between the pixel in question and those in the sampling window. The sampling window can be whatever you define, a square, an annulus, something extracted from another element map or image.

https://en.wikipedia.org/wiki/Moran's_I

https://en.wikipedia.org/wiki/Geary's_C

[Probeman]

Would there be any utility in implementing a spatial autocorrelation algorithm like Moran's I, or Geary's C?

Geary's C might be more useful as you can move a sampling window over the image to see examine the correlation between the pixel in question and those in the sampling window. The sampling window can be whatever you define, a square, an annulus, something extracted from another element map or image.

https://en.wikipedia.org/wiki/Moran's_I

https://en.wikipedia.org/wiki/Geary's_C

Hi Jeremy,
I would guess that there is, but the question is: how should it be implemented in the CalcImage GUI?  I can think of lots of bad ways to do it, and several good ways, but perhaps we should skype and chat about it sometime?

Let me know by email when a good time for you is.
john