Reaching for some signal
At the Center for Advanced Molecular Imaging, I’m fortunate to do science outreach with a variety of visitors. I enjoy the gifted high school students because they often amaze me with their curious minds. The images below are part of a demonstration we did for a group of high schools students. It’s a simple example of boosting your signal-to-noise ratio (SNR) by signal averaging.
Part of the demo explains how MRI works, which I won’t go into. You can check out my MRI 101 post if you missed it. The image on the left was averaged 4 times and the image on the right was not averaged at all.
The blue and cyan regions of interest (ROI) were used to measure the noise, which is assumed to be random rather than coherent/systematic. The red ROI is a representative sample of signal. It’s important that the ROIs are the same size for some discussions of SNR. Note, because the non-averaged image has more noise, my software that automagically identifies the sample (denoted by the yellow ROI), included the smaller sample, i.e., the software fails to see two objects. The software has correctly selected the larger of the two samples due to less noise in the left image.
After averaging the image four times, the SNR is 9.2. Compare that to 4.9 with no averaging. As expected the random noise averages out, increasing the SNR. You can see that we did not get a 4x increase in SNR. So you have a trade-off of increasing image acquisition time and return on that investment in terms of improved SNR. What we can teach the students in this quick demo is that you reach a point of diminishing returns.
If you consider the SNR of the whole sample, it’s 2.8 with averaging and 4.6 without? Wait, why is it worse with averaging? This is due to the software including more “signal” in the non-averaged image. So we are comparing the ratio of two different sample sizes. I intentionally didn’t fix the sample ROI to make this point.
If you liked the #ISeeTheWorldWithScience series that some of us scientists on G+ have been contributing to, you are welcome to guess what the sample is or tell me some cool science that you see. The small sample on the left is different than the big sample on the right.
Previous examples of #ISeeTheWorldWithScience
http://goo.gl/98ZhNL via +Mark Crowley
http://goo.gl/kPz2Kr via +Rajini Rao
http://goo.gl/3nhaI4 via +Johnathan Chung
Medical Imaging 101 pt 3: MRI (http://goo.gl/UVbiU)
Happy #ScienceSunday
Keep posting good science and interact with questions to have better SNR on G+.
Edit I forgot to mention that the 20′ interactive 3D wall helps get the students attention. http://goo.gl/oV8q8Z
The smoothing out of noise (probably did not say that right!) makes a huge difference. Thanks for the explanation, Chad.
You are welcome Rajini Rao I bet you know what both samples are.
Uh oh. Can I blame the absence of scale? It looks rather myelin sheath-ish.
No myelin on these but you might find quercetin Rajini Rao
I assumed it was animal and not vegetal, darn!!
An onion??
Sort of.
Hmmm….Allium sp. ?
Sorry I meant what type of onion. The shapes and interior should help.
Getting warmer, yay. Garlic pods or spring onion?
Scallion and what’s on the right?
You mean the larger blob to the right? Both photos are the same, no?
The right half of the images.
The shape of a garlic clove was a good guess Rajini Rao
Aha! 🙂 I guess it could have been a shallot as well.
So what type of onion is shaped like a garlic clove?
Wow, I thought I had exhausted them all. I did mention shallots. Edibles Alliums are: Onion, scallions, garlic, shallots, leeks, chives. One of those?
Shallot 🙂
“Thanks a lot”, said Sean Connery.