Noise Is Your Friend

By Ctein

No, really.

You think I'd lie about something like that?

Noise is the bête noire of both the idealist and the fetishistic pixel peeper, but in the real world appropriate levels of noise improve signals.

Ears use noise to improve their sensitivity. There's a signal threshold below which a hair cell in the inner ear won't respond (else we'd be deafened by the din of molecular vibration). Yet, those cells respond to audio signals several dB below that threshold, because random noise in the system mixes with the signal and occasionally kicks it up above the cell's threshold. The response isn't anything like clean, but a static-degraded response is better than none at all.

Most computer printers produce no more than a handful of gray levels. The way they generate the illusion of continuous tone is by injecting arithmetical noise (random numbers) into the process of deciding whether or not to lay down an ink droplet. The probability that any droplet will be laid down depends on the strength of the signal, but it wouldn't be a probabilistic matter at all were it not for the noise.

Digital cameras benefit greatly from a little noise. I can illustrate why in the accompanying figure. The top bar is just an ordinary continuous gradient from black to white: this is our stand-in for a real-world scene. I've expanded the shadow detail, bracketed by the blue lines, to full image width in the second row, for scale. Since the tones are all near-black, you probably can't see any difference on your screen, but I'll fix that.

In the bottom three rows, I've expanded the gray scale only in the illustration, so you can see the gradient in the shadows. In other words, the gradient in the third row is really the same as the second row—you're just kind of viewing it through a contrast-magnifying glass.

Now, what happens when you digitize that shadow range with a hypothetical noise-free camera? You get the fourth row in the illustration. (remember that this is still really covering the same tonal range as the second row.) The continuous grayscale ends up being mapped to a baker's dozen of sharply defined gray levels. Were a photographer trying to enhance the shadow detail in this "scene," they'd have spurious banding and very poor tonal rendition.

Suppose the camera were a little noisy, as it will be in the real world? That's what the bottom row shows: I injected a low level of noise into the original gradient before digitizing it. That is, the fourth and fifth rows have had exactly the same conversions and presentations. The only difference is in the system noise.

I trust I've made my point.

Too much noise is a bad thing...true of most things in the real world. But little bit of noise? That's a very, very good thing!

Ctein

Featured Comment by richardplondon: "I think it sheds more light to talk about quantisation than digitisation. Every aspect of what we do digitally with images is subject to this.

"But: we have no completely clean data, analog or digital, anyway—unless we make it so artificially (through active noise reduction). Photons are not nicely behaved—they are little scamps. Only a very tiny degree of jitter is ever deliberately introduced in digital applications (to reduce quantisation artefacts), and I don't think this is being proposed here; not necessary.

"I read this useful article as signifying that we should not officiously clean up digital source data with noise reduction, to the point where we would start to see these other unpleasant artifacts.

"Shot noise, for example, is a true record of the way that some actual light sprinkled onto the sensor. It is authenticity—reality—just as film grains are. Of course we all hope at the same time that read noise and other processing errors are improvable, just as with film grain size/clumping."

Comments

[Awake]

So noise reduces banding in the example, but isn't that also reducing resolution? Unless I am misunderstanding the text, the third row is expected to have steps, because the first image was created in steps. The fourth image has no steps, even though it should have them??? Has the noise in a sense introduced 'blurring'?

If we had an infinite number of steps, then there would be no banding... so doesn't just affirm the case for using more digital bits per sample, as in keeping an image in 16 bit (or even 24 bit) mode rather than 8 bit mode?

[mikeinmagog]

I'm going to run this by my good friends at DPR and see what they think.

[Miserere]

Ctein,

Hopefully the noise of a thousand TOP readers clapping at the same time will excite your auditory hair cells.

T$ha#nk *yo&u,

—M.

[Jeff S]

I've always added noise to most of my prints. Not for any technical reason, but just because it looked "natural" to me.

[James Kingdon]

I knew I'd seen this idea discussed before, but boy did it take some tracking down!

If you want a really deep dive have a look at this brain twisting article by Emil Martinec:

http://theory.uchicago.edu/~ejm/pix/20d/tests/noise/index.html

The neat illustrations of noise vs posterization come on page 3.

James.

[Chris Gibbs]

Ctein,

I do agree with you wholeheartedly - a little noise is a good thing. Jeff Schewe has written to this extensively, especially when up-sampling image files.

Paper choice too - the surface texture on Crane & Co's Museo Silver Rag has a very similar effect, but on the back end!

[ctein]

Dear Mikeinmagagog,

DPR?

Department of Parks and Recreation???

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Dear Awake,

Yes, you have misunderstood a bit. [Ctein has now changed the post to help answer your question --MJ.]

The original gradient was created at a very high bit depth, so it's effectively continuous tone. Ditto, the second row in the illustration-- it really has thousand of discrete tonal steps in it.

The continuous tone can't really be illustrated in Rows 1 and 2 because the JPEG is only 8 bits deep. (And, yes, it did take me a bit of thinking to come up with a demo illustration that wouldn't get screwed up by converting it to a JPEG.)

If I had expanded the brightness scale of row 2 without digitizing it, what you would see in the illustration would be a "continuous" tone gradient running from black to light grey. It was the act of digitizing it down to 8 bits that produced the broad banding you see in Row 4. Those bands do not exist in the original image--they're entirely an artifact of bit depth reduction.

Did this help clear things up?

pax / Ctein

[Janne]

Noise has another effect: it stands in for the fine detail that spatial sampling removes. Our eyes expect to see the effect of near-threshold and subthreshold detail in the scene; that's part of what we use to determine surface qualities and it's also what our eyes use to determine whether they're in focus or not.

So objects in a completely smooth image will tend to look like plastic - plastics typically have very little of this microstructure in real life. And noise-free images will tend to look less sharp and just a little out of focus since our eyes don't get the expected noise-like fine structure input that tells the brain the eyes are in focus.

[James Jones]

In recording music, noise is an important component for the same reasons and is sometimes added for better dithering.

[Bahi]

Very effective illustration, Ctein.

Agreed also with Janne: the presence of fine noise is one of the many mechanisms by which a photograph can succeed by failing gracefully. If there's only a hint of sharp detail and some pleasant luminance noise, the imagination is often able and willing to fill in the missing information at some level. The noise serves as permission, like the texture of canvas on a painting. But only a hint of sharp detail with no base texture to excuse the absence of the rest… meh.

[robert e]

Weird. I was just about to query whether "permission to dither" roughly sums up the benefits of noise according to Ctein, above. Then I scroll down to Bahi's theory that noise gives people "permission to imagine".

[Josef Tornick]

That is totally illuminating. Thanks for the great article!

[Bill]

These arguments only hold for the approximation that is digitization. One should not conclude that analog signals are also enhanced by adding noise.

Adding noise is an ad hoc means of modeling the information that is lost in order to enjoy the convenience of data in digital format.

[hugh crawford]

I'm glad to see the discussion of noise open up here, and especially the comparisons with audio recording.

Slightly off topic though, how about a consideration of noise as an aesthetic tool?

I very often apply sharpening at one third and two thirds of a pixel radius just to bring up the the noise a little, much like my favorite development of D-19 diluted one to one for any B&W film. This gives me a high frequency noise that looks much more pleasing than the photoshop "adding noise" filter which is quite ugly.

One of the main reasons I have for working with raw files is that I can avoid the in camera ( in both senses of the term ) noise reduction. Canon's noise reduction is to my eye particularly ugly and intrusive. Inspired by Mike's listing of a Canon point and shoot as one of the Top Ten, and the availability of the CHDK software to reprogram the firmware of canon point and shoot cameras, I have been experimenting with a sd1100 reprogrammed to shoot in raw and sometimes use it at ISO 8000. I've got to say that it looks better without noise reduction then it does with.

I'd like to see a qualitative discussion of noise as opposed to the quantitative "all noise is bad" discussion that has been the norm till now.

Sort of like the treatment of "Bokeh" perhaps?

[sv1en]

Bill,

Your statement that noise optimizes only the digitization of signals and that analog signals are not enhanced by noise is not completely true.

You might want to look at this article (available also through the author's website in Augsburg University):

P. Hänggi
Stochastic Resonance in Biology
ChemPhysChem. 3, 285–290 (2002)

(The article is actually quite accessible to anybody with basic highschool knowledge in natural sciences.)

It is amazing how much noise plays a role in perception and the action of neurons (Ctein hints at that in his article).

... and now: back to photography ...

[PWP]

Yes, Ctein, this makes perfect sense.

My company made noise reduction devices to enhance radio communications and we found that speech intelligibility was improved when not all of the noise was removed. In fact, we ended up generating consistent white noise and adding a small amount back into the noise-reduced audio. I should add that this occurred in the analog domain.

[Leslie Clement]

This is true in the printing world as well. We always add a slight amount of noise to a gradient so that the banding you speak of does not occur.

[hugh crawford]

Another interesting topic would be how noise or schotastic dithering can increase perceived resolution when detail approaches the Shannon-Nyquist limit. I noticed that in the Sigma DP-2 examples of the truck in the next posting that there is both a lack of noise , and some nasty aliasing of nearly horizontal lines.

[Peter Klein]

Ctein: Thank you, thank you, thank you! You've put a little-known truth into layman's terms. Of course, it runs counter to what the average person "knows." And it will be met with scorn by Internet pixel-peepers, who like being able to eyeball noise at 100% magnification and have easy proof of a camera or photograph's inferiority.

What matters is how much noise there is at print size or screen-viewing size, the character of that noise, and whether it enhances or detracts from the visual effect desired.

[Neil Fiertel]

Dithering is essentially what we are talking about which is basic to digital recording of sound and it is no different with visual files..numbers are numbers. For those that somehow think that analog is somehow superior and does not have the perceived defects requiring dither or noise, the reality is that film itself has a built in dither as any film developed after even a flat lighting image is exposed will show random crystal clumping determined by temperature, developer type, film type and so forth. In fact, I wrote a paper on this very subject in 1958 for the Westinghouse Talent Search ( ha ha..I was a finalist..no money but a picture in the local paper!) It was called "Crystal Clumping in an Ionic Solution is Related to Temperature" In other words, noise is nothing new and without it film also looks soft. I used to shoot Dokupan which had an ASA ( old name for ISO) that was about 4 and was about as grainless as one could imagine and guess what..it looked soft even with glorious details that it also had. I thought for a while it was the lack of lens quality but when I experimented with shooting the identical image with the same equipment with Pan X it looked sharper...that tiny bit of grain did it...dither wins again..It is the dither that our eyes require for the perception of sharpness.

[Brad Nichol]

Yep, great to see this article. I have added noise to pretty much all my own exhibition works and it has allowed me to enlarge small low res files (3 megapixel in many cases) to quite large sizes 20 by 24 inches for example. This of course is done in conjunction with a lot of other tricks, but added noise is the key!

Noise creates the impression of detail, tonal gradation and done well just looks really good at normal viewing distances.

I have no doubt low noise pixel peepers will be challenged by this article, but frankly the no noise approach is a plastic dead end and in real world prints files from cameras that are actually a little noisy often look far more realistic and have greater impact.

[Maxim Muir]

Ctein,

Back in the film days, I "discovered" that prints needed grain to have additional edges for your eyes to focus upon at the contrast boundaries, and create the impression of sharpness. This is why I never liked the look of Panatomic-X or Ilford Pan F 35mm negatives compared to say Tr-X or Ilford HP5 negatives-the prints from the grainier, faster films always looked crisper. Of course, they would not print the same due to the differences in the characteristic curves, but a good printer knew how to fix that.

And don't get me started on how terrible prints from Tech Pan negatives looked. I got several Gamma .55 associates off that stuff and onto larger format film:)

[ctein]

Dear James,

Thanks for the pointer to Emil's webpage. That's SERIOUSLY nice! I also really liked his analysis of noise versus bit depth versus ISO versus exposure. I've bookmarked it for permanent reference.

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Dear Richard,

I agree with you, technically. I don't think it's more useful for the readers; they don't directly deal with quantization.

Any sensing system that has a threshold or quantizes a signal is going to benefit from small amounts of noise. Digital systems do both. A lot of analog systems do one and/or the other. Traditional photographic systems have a strong threshold; Mike and I had a little conversation about that in private. There have been various sorts of technology hacks that throw a little noise into the photographic system; done properly, they could substantially improve sensitivity and exposure range.

~ pax \ Ctein
[ Please excuse any word-salad. MacSpeech in training! ]
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