January 28, 2001

7:50 PM

There's been a lot of talk of late about signal-to-noise ratios here on MeFi (er, Ashcroft who?...). Generally, we think of noise as something that always degrades the quality of a signal. Sometimes, however, the opposite can be the case. Here's a neat little demonstration of a non-linear system in which noise can be used to amplify a signal that would otherwise be too be faint to detect any other way. It exploits a phenomenon known as Stochastic Resonance.
posted by lagado (25 comments total)

So I received this story on stochastic resonance in my email this morning from the American Institute of Physics update. Unfortuantely no link (other than www.aip.org), so I'm reporoducing it in full here:

HOW RANDOM NOISE COULD BETRAY AN ARMY'S
OUTPOST. New research adds plausibility to the notion that
living things make use of random electrical noise to optimize
specific behavioral responses. To test this hypothesis of
"behavioral stochastic resonance," researchers have been studying
the paddlefish Polyodon spathula, a primitive creature whose fossil
record extends back 65 million years. Found only in the river
basins of the Midwestern United States and China's Yangtze river,
the paddlefish feeds exclusively on the zooplankton Daphnia, a
plankton 1-2 mm in length. Catching Daphnia mainly at the
bottom of silty waters where visibility is low, the paddlefish relies
upon electric-field receptors in its rostrum (a paddle-shaped nose-
like appendage) to detect electric signals emitted by the plankton,
whose swimming and feeding motions result in the firing of nerve
cells. In an earlier experiment (Russell et al., Nature, 18
November 1999), researchers showed that adding an intermediate
amount of external noise in the vicinity of a juvenile paddlefish
could improve its ability to detect and capture plankton. Now,
some of the same researchers (Frank Moss, University of Missouri
at St. Louis, 314-516-6150, [e-mail] and Lutz
Schimansky-Geier, Humboldt University in Berlin,
[e-mail], and their colleagues) have
calculated that a swarm of plankton can generate enough noise by
themselves to amplify electrical signals from a single Daphnia
ordinarily too weak for the paddlefish to detect, thereby betraying
its presence and enabling the paddlefish to detect and capture it.
This work adds evidence to the idea that stochastic resonance has
been adapted by living creatures in their evolution, and makes
progress towards designing a definitive behavioral experiment to
test this hypothesis. (Freund et al., Phys. Rev. E, Mar. 2001; pdf
version not yet ready but we can fax the article to journalists.)

posted by lagado at 7:58 PM on January 28, 2001

Wow. Not only relevant but incredibly cool science. So, how do we use the Ashcroft posts to improve the meaning of MetaFliter? ;)
posted by kindall at 8:17 PM on January 28, 2001

That's actually incredibly cool. I vote for this for most interesting post on MeFi this month.

So, what can we *do* with it? :-)
posted by baylink at 8:21 PM on January 28, 2001

What can we learn from this? Well, I think it's now clear that 40 posts/comments about Ashcroft, Nader, or GWBush aren't enough, that 120 make the issue much more clear, but 400 are a bit too much.

:)
posted by mathowie at 8:22 PM on January 28, 2001

And an occasional smart-ass comment from a Dennis Miller Wannabe doesn't spoil the whole thread...
And if you really want to check out a "signal-to-noise" ratio, try standing in the middle a traffic intersection with a "three-way" light and throw small objects at the cars.
posted by wendell at 8:30 PM on January 28, 2001

I don't get , "single-to-noise".
posted by ojsbuddy at 9:25 PM on January 28, 2001

We single people refer to married people as "noise" because all they can talk about is their kids. The "single-to-noise" ratio is an indication of the proportion of single people, and thus the likelihood of intelligent conversation. (Conversation to a married person consists of "yes dear" and not much else.)
posted by Steven Den Beste at 9:34 PM on January 28, 2001

Signal-to-noise is an engineering term that describes the ratio of the stuff you want (signal) to the stuff you don't (noise). If the signal-to-noise ratio is low on an audio signal, for example, you get lots of static and hiss. With video signals it means snow and other picture problems. With digital signals it means lots of re-transmissions to get the data through.

Extended to human interaction, "low signal-to-noise" just means that there's a lot of talk about stuff you're not interested in, relative to the amount of stuff you are, which makes it difficult to find the stuff you're interested in.
posted by kindall at 9:37 PM on January 28, 2001

Here's a related comment from Brian Eno:

"Noise is unreadable, inscrutable…Noise is the signature of unpredictability, outsideness, uncontrolledness…Our history of music would chart the evolution and triumph of noise over purity in music…Rock music is built on distortion: on the idea that things are enriched, not degraded, by noise. To allow something to become noisy is to allow it to support multiple readings. It is a way of multiplying resonances."
A Year With Swollen Appendices

How this applies to saturation posting, I'm not sure. . . But re-defining "noise" is interesting. . . and fun to listen to, in a musical context.

posted by aflakete at 9:42 PM on January 28, 2001

We single people refer to married people as "noise" because all they can talk about is their kids

I thoroughly resemble that statement!
posted by lagado at 9:59 PM on January 28, 2001

Regarding Aflakete's posted Eno quote: you may also be interested in the work of William Paulson, who applies those same ideas to literature. He sees literature as a "noisy" means of using language to transmit information, but he sees that noisiness as contributing to literature's ability to survive through the ages (since the noise supports "multiple readings," to use Eno's terms).

Interested parties may wish to check out this book (usually ships in 4-6 weeks).

Does this mean that Metafilter is the literature of the future? (Scary.)


posted by jbushnell at 10:12 PM on January 28, 2001

Okay, so I went to the link, saw the demonstration, and was suitably impressed, but the explanation left a lot to be desired. Can anyone explain the following to me:

1) Obviously, the images and the simulation of the effect of stochastic resonance on the grayscale picture are jpegs or gifs, which are compressed. Are the experiments being done on the original bitmaps and the results compressed for our viewing, or can the experiments actually work even on compressed files?

2) What does the image look like without any additional noise?

3) Stochastic resonance (from what I was able to glean from articles found quickly on the web) involves a sine wave driving force and an additional white, Gaussian noise driving force to drive classical particles from one potential well to another. The non-linear bit comes in when you see that the resonance doesn't increase linearly with the noise amplitude. Here's what I don't get: what would the potential wells be in this case? Are they "black" and "white", and the noise allows for information to be mined from pixels that are various shades of gray by our ability to focus on a time-averaged picture? If so, wouldn't that mean that the information could be obtained by using a different static filter on the original picture?

Any physicists/mathematicians/computer scientists out there want to explain this to us laymen?
posted by UrineSoakedRube at 8:47 AM on January 29, 2001

In an earlier experiment, researchers showed that adding an intermediate amount of external noise in the vicinity of a juvenile paddlefish could improve its ability to detect and capture plankton. Now, some of the same researchers have calculated that a swarm of plankton can generate enough noise by themselves to amplify electrical signals from a single Daphnia ordinarily too weak for the paddlefish to detect, thereby betraying its presence and enabling the paddlefish to detect and capture it. This work adds evidence to the idea that stochastic resonance has been adapted by living creatures in their evolution, and makes progress towards designing a definitive behavioral experiment to test this hypothesis. (cites deleted)

Okay, what does this mean? I understand how the signals from the swarm (the noise) can make a single Daphnia (the signal) easier to detect. How is this evidence that stochastic resonance has been adapted by predators via natural selection? What special ability does the paddlefish have that allows it to detect a signal amplified via stochastic resonance, but not a signal amplified via any other method?
posted by UrineSoakedRube at 9:02 AM on January 29, 2001

I don't know that it's evidence per se, but stochastic resonance appears to be (to me) an analog of natural selection.
posted by sonofsamiam at 9:25 AM on January 29, 2001

sonofsamiam>I don't know that it's evidence per se, but stochastic resonance appears to be (to me) an analog of natural selection.

But that doesn't appear to be what the paddlefish researchers are saying. They seem to be arguing that the paddlefish has evolved in response to evolutionary pressures to be able to use stochastic resonance to catch Daphnia. They aren't saying that stochastic resonance in selection pressures caused the paddlefish to evolve in a certain way. Which brings up the question: what specific ability does the paddlefish have that allows it to detect stochastic resonance-enhanced signals (as opposed to generally amplified signals)?
posted by UrineSoakedRube at 9:38 AM on January 29, 2001

Ah. I see, I misread.
I'd guess that the extra noise can maybe... I dunno, allow them to approximate the location of plankton, and then hone down their location.
posted by sonofsamiam at 9:44 AM on January 29, 2001

sonofsamiam>Ah. I see, I misread. I'd guess that the extra noise can maybe... I dunno, allow them to approximate the location of plankton, and then hone down their location.

Okay, I understand that they can use the phenomenon of stochastic resonance to find single Daphnia, but is this actually a special ability? With the grayscale picture demo, the question would be if we have a special ability to detect stochastic resonance-enhanced signals because of some intrinsic quality of our brains, or if we have a general ability to detect signals, and if they are enhanced (via stochastic resonance or any other amplification method) we are more likely to detect them. I guess I don't see what either example has to do with specific evolutionary pressures.
posted by UrineSoakedRube at 9:52 AM on January 29, 2001

Okay, I see what you're getting at. Yeah, I'd agree, they don't mention any actual link that shows that this particular brand of reception is produced by natural selection.
posted by sonofsamiam at 12:14 PM on January 29, 2001

I believe the distinction called for here is that it's not necessary that the amplification be from SR for it to be useful in the various contexts.

SR merely happens to work, and may be the only available means *of* amplification. That better?
posted by baylink at 12:23 PM on January 29, 2001

sonofsamiam>Okay, I see what you're getting at. Yeah, I'd agree, they don't mention any actual link that shows that this particular brand of reception is produced by natural selection.

Yeah, it does seem kind of strange. I understand the basic mathematical/physical model, with the harmonic driving force, the Gaussian random white noise, the potential wells, and the classical particles. At least, I think I do. I just don't understand some of the analogues in the two examples mentioned.

By the way, this conversation we've been having seems to have driven away everyone else. And we didn't even have to mention Hitler!
posted by UrineSoakedRube at 12:23 PM on January 29, 2001

baylink>I believe the distinction called for here is that it's not necessary that the amplification be from SR for it to be useful in the various contexts.

SR merely happens to work, and may be the only available means *of* amplification. That better?

Which returns us to the question of why the researchers say that "stochastic resonance has been adapted" by the paddlefish, instead of being "used". Maybe someone should pretend to be a journalist and get a copy of that article from them.
posted by UrineSoakedRube at 1:18 PM on January 29, 2001

The article is saying that stochastic resonance, which is a phenemonon that has been understood for some time in artificial systems, seems to be the most likely way that paddlefish detect their prey. This is evidence but certainly not proof.

1) Obviously, the images and the simulation of the effect of stochastic resonance on the grayscale picture are jpegs or gifs, which are compressed. Are the experiments being done on the original bitmaps and the results compressed for our viewing, or can the experiments actually work even on compressed files?

2) What does the image look like without any additional noise?

3) Stochastic resonance (from what I was able to glean from articles found quickly on the web) involves a sine wave driving force and an additional white, Gaussian noise driving force to drive classical particles from one potential well to another. The non-linear bit comes in when you see that the resonance doesn't increase linearly with the noise amplitude. Here's what I don't get: what would the potential wells be in this case? Are they "black" and "white", and the noise allows for information to be mined from pixels that are various shades of gray by our ability to focus on a time-averaged picture? If so, wouldn't that mean that the information could be obtained by using a different static filter on the original picture?

1. Compression doesn't have anything to do with it. It would work just fine with uncompressed bitmaps.

2. What would it look like without additional noise? Black probably. All the grey information would be lost. The original (dark) grey scale image signal is being shown through a non-linear threshhold filter which basically drops out everything.

3. Generally filters lose information not gain it. Stochastic resonance obtains more information than a static filter can by itself because the noise is adding to the signal enough amplitude to push random bits of it over the threshold. The effect is equivalent to shifting bits of the signal up the y axis and over the threshold. It's also shifting information into the time domain, you only get the whole picture over time.

Other amplification techniques exist but they also amplify the noise. This technique exploits resonance to remove the noise from the image.

posted by lagado at 5:07 PM on January 29, 2001

lagado>2. What would it look like without additional noise? Black probably. All the grey information would be lost. The original (dark) grey scale image signal is being shown through a non-linear threshhold filter which basically drops out everything.

Okay, let's see if I understand this. If I were to look at the original picture, I'd see only black, because of the filters. All right, suppose I took the bitmap of the original picture and assigned one of 256 (or more) shades of gray to each pixel based on how light or dark it was. Given that this filter is less drastic than the threshold filter, wouldn't I be able to make out much of the signal? Why or why not?

3. Generally filters lose information not gain it. Stochastic resonance obtains more information than a static filter can by itself because the noise is adding to the signal enough amplitude to push random bits of it over the threshold. The effect is equivalent to shifting bits of the signal up the y axis and over the threshold. It's also shifting information into the time domain, you only get the whole picture over time.

Other amplification techniques exist but they also amplify the noise. This technique exploits resonance to remove the noise from the image.

I understand that stochastic resonance does work in this case (although I think the explanation of the phenomenon is less than clear). I also understand that there are cases where stochastic resonance may be the only available amplification method. What isn't clear to me is that one can extract more information in this case from stochastic resonance than from using a less drastic filter (many shades of gray instead of a threshold black/white filter).

Basically, it seems that the demo site is positing a comparison between: 1) what the human eye can see when looking at a grayscale picture that has been threshold filtered almost entirely into the black, and 2) what the human eye can see once stochastic resonance has been applied to the unfiltered grayscale picture, then rendered in black and white. What you get by looking at the time-averaged picture seems to be pretty much what you'd get by looking at an unfiltered grayscale bitmap.


posted by UrineSoakedRube at 7:13 AM on January 30, 2001

Sorry for the delay, I didn't see your reply until just now.

The point is that we are trying to amplify a weak signal which is swamped by a noisy environment. The noise is not optional nor is the strength of the signal, you're a paddlefish looking for plankton on a muddy river bottom, right? ;-j

Say your original signal ranged between 0 and 255, fine. Now imagine adding noise that also ranged between 0 and 255. The noisy plus signal now ranges between 0 and 511. So how do you amplify the original signal and reduce the noise?

Answer: Tresholding and time averaging.
posted by lagado at 3:58 PM on January 31, 2001

One last take on noise:

"Communications without intelligence is noise;  Intelligence
without communications is irrelevant." Gen Alfred. M. Gray, USMC

Even Marine speech patterns are ERECT. . .

(quote from cryptome.org)
posted by aflakete at 8:57 PM on February 1, 2001