What Is Noise?
(A much more serious and mysterious question than most will realize...)
In my (mostly former) career, writing books about astrophotography, there was one subject that confused more people than any other: noise in photographs.
Most take for granted that noise is the grain in a photograph. But: no. That’s not noise.
Or many will think of noise in an audio recording (and most of these people remember vinyl records, and that scratchy sound they made after being played a few times). But: no. That’s not noise in the scientific sense.
So what is noise? And why would anyone care in the digital era when there is no noise like that? (But: no, that’s not true, either.)
Here is something that looks like a very noisy photograph:
It’s dark, it doesn’t look like it has a great deal of detail, and some of the stars are not round—this image has a lot of problems, but noise is not one of them.
THIS is a noisy photo:
Is it noisy because it’s red? No; that’s from dust in the air. “Please, please, Mr. Writer: WTF are you talking about, and why are you being so obtuse!!!”
In order to be less obtuse, I’m going to take a few steps back. Here is that same noisy image with all of the noise much more visible by making the image brighter:
Here is a blow-up of a portion of that noisy image:
The technical definition of noise is “the uncertainty in the data.” What color is the background, for example. Red? Green? Blue? Every pixel is a different color than the ones next to it. Those variations tell us that noise is present: the color of the background is uncertain at each pixel.
The same is true of the pixels where the galaxy image is recorded. They look sort of cream-colored, but there’s a lot of color confusion as well. But it’s not just the color; the brightness is also very noisy:
You can see hints of the structure of the galaxy, but the noise prevents getting an accurate idea.
What about removing noise? Well, there are two ways to do that, and one of them is a complete and utter lie:
* You can get more information; if you have more information, you have less uncertainty and thus less noise. In this case, taking a longer exposure or taking multiple exposure and combining them (that is, averaging them over time) would both reduce the noise level in the data.
* You can smooth the image. This doesn’t lower the noise, however; it just averages it out across the space of the image. If there are two pixels, and one is brighter than the other, we can make both pixels the same brightness as their average.
So real noise reduction is a matter of getting more data; pretend noise reduction is smoothing things out to hide the noise.
The image at the top, which looks reasonably smooth, is a case of false noise reduction. I just smoothed over it. No amount of smoothing will make up for the high level of noise. This becomes abundantly clear when you see just how much information is missing from my images—take a look at this image European Southern Observaotory.
Noise is lost information; it can’t be replaced, it can only be covered up. Everything is noisy, but if you have enough signal, the noise will be small in comparison, like the ESO image linked above. A photograph taken in sunlight will be rich with signal and it will show a lot of detail. A photograph taken at night in the back yard will be poor in signal, and noise will dominate.
Why is all this important? If you are doing science, especially modern science, a huge part of your job is get lots of signal and to isolate and avoid sources of noise. If you want to identify proteins in a cell, then you need to isolate them to a very high degree. If you want to sense gravity waves from colliding black holes, then you have to understand all the movements that constitute noise and find ways to deal with them so you can get some useful signal. (long baselines; high precision; buried in rock, and so on)
Modern science is built on a true understanding of what noise is and how to improve signal. You can remove noise; noise is the signal that’s missing, that’s badly recorded, that’s hidden by similar signals, etc. Noise is the uncertainty—not a thing you can measure, it is what you can’t measure, the error.
As humans, we inherit the terrible power to hide our errors, to ignore them, to, as it were, make up the signal we want to find. Don’t be a fool, please; we are all together in the enterprise of surviving on this planet.