Why is the signal to noise ratio (SNR) so confusing for me?

Question

I don't understand SNR. When I read Wiki (ofcourse the best reference on earth ;) ) - It saids that it is the ratio of meaningful information to noise. I need to use SNR with imaging modalities. And this is confusing because many things happen during the imaging process. For example a CT or MRI scanner has very complicated techniques to reconstruct the picture from the basic signals. It may use filtering, averaging, back projection, interpolation -who knows what more... but the original signal- information is manipulated: So at what stage should you measure SNR if you want it to reflect the qualitity of your imaging modality?

Another strange thing is that the SNR seems to reflect more what I am measuring rather than the measuring apparatus itself. For example if I measure velocity with something- the faster the thing goes the more signal I may get: so a higher SNR. -but this says nothing about the measurement apparatus itself.

Please help me to understand SNR.

Answer 1

Noise and resolution are complementary concepts in imaging. In an imaging system, noise is a local property measuring how much variation there is from pixel to pixel, even it the target itself is uniform. Resolution is how far apart two lines with widths equal to their separation have to be for you to tell it's two lines instead of one. The two are related; smoothing th image to reduce noise decreases resolution. One result of this trade-off is that increasing contrast (thereby making it stand higher above the noise) improves the maximum resolution achievable by filtering.

When you image is bases on data inversion, like CT, things become even more complicated because artifacts can be introduced. This are well resolved things generated by the inversion procedure that stand out above the noise, but are not part of the target. Filtering in inversion techniques is performed using singular value decomposition techniques and/or first or second order regularization. That's big-head math stuff you can research. Here'a book to get you started.

Answer 2

SNR is a good measure of signal quality in communication channels with Gaussian noise. In any other scenario, especially something as complicated as an MRI, a physicist would probably prefer to do a real error analysis.

SNR does not say anything about your apparatus. It is simply a ratio between signal energy and noise energy in your signal. Nothing more, nothing less. But like I said, it is probably not a good measure for your system. So why use it?

Answer 3

Your basic question, when it comes down to it, is how to define the SNR to reflect the quality of your processing. SNR can be measured at any point in the signal path; the quality of the signal processing is reflected in the improvement in SNR between the raw, unprocessed signal and the final product.

The area I'm most familiar with is communications technology: in spread spectrum communications we can start with a signal that is so low compared to the noise floor that the SNR is measured in negative decibels (i.e. the signal is actually overcome by the noise). However, since the signal is time or code correlated, while the noise is not, we can process the signal to vastly improve the SNR to the point where the signal is clearly distinguishable from the noise, and therefore simpler to decode.

Answer 4

You are correct, as the speed increase the signal increase.
The noise (+/- 5 mph for example) will also grow usually.
So the SNR might be almost constant over the whole spped range.
A radar might have +/- 5% so the SNR is 5% all the time.
Some measurements might not have constant SNR and it is more apparent for low signals.
It depends on the peasurement apparatus and the measurement.