We all have an intuitive understanding of what noise is; so let’s start with that.  You’re sitting in a restaurant, and your boyfriend is about to propose to you.  The problem is that you’re having trouble hearing him, because of all the noise around you – the self-impressed boorish lout at the next table gfawing loudly at his own jokes, the children screaming on the other side of the room, and the large table full of intoxicated people all talking at once. Your boyfriend is nervous and speaking unusually softly.  So we have it – first background noise and second a low signal.

Engineers describe this as the signal-to-noise ratio.  When this ratio becomes less than about one, the signal becomes very hard to discern above the noise.  And recognize, that it’s not just that there is a background that’s the problem, the problem is that it varies and is random.  Your ears and your brain just don’t know how to process the sound to separate the signal from the noise.  Note, that I’m trying to distinguish between background, which if it is constant, can be easily dealt with, and noise which is random.

Let’s return to the restaurant, somebody steps up to the front of the room and starts talking into a microphone.  Suddenly, there’s a signal that is way above the noise, has a high signal-to-noise ratio, and is easily discerned.  Wait a minute you say, what about my proposal.  I’llk leave that for you to figure out.

Have you ever heard someone speak or sing into a microphone that has a loose connection that causes the amplification to vary randomly?  Sometimes the sound is high above the background and sometimes it’s low and near the background.  Well, that’s another type of noise, called signal noise.  The total noise in a system is the combination of the background noise and the signal noise.  In fact, every component of a system, say a camera system, can introduce noise.

Optical systems, like cameras, have the same issues.  For instance, fog introduces noise into your image, making it hard to see things.  It reduces the contrast.  Now in my blog of October 20, 2012, we discussed the relationship between image resolution and contrast.  Contrast is the difference between white and black.  The finer detail you want to see, the more contrast you need.  We have defined resolution in terms of the finest line separation you can still discern.  If you make it harder to discern the lines by adding noise, both to the white signal and to the black background, your resolution decreases.

By the way, I do hope that the proposal worked out!