Noise is Good: No, Really – Noise Can Be Very Useful

Some of my best ideas for new postings come from reading my colleagues’ LockerGnome postings. In particular, Ron Schenone recently posted a piece about how to tell if a photo has been altered. Since I have spent a lot of time restoring damaged photos, and even had some of my work published, detecting what someone else has done to photos has always been a puzzle. How do you decide if a photo is pristine? Once you have developed some competence with Photoshop or GIMP, you start to look at other people’s photos a little differently. Sometimes you only have a nagging feeling that “something is not quite right.” But how can you tell for sure? One surprising answer is to consider the noise in an image. Noise is the random fluctuations that, in a good image, are small enough that you do not notice them — but noise is always present.

Studying noise in images might seem like a strange way to detect image manipulation, or do anything good, but it can be used to detect manipulation and even to study nature in surprising ways. Noise is not always an unwanted intrusion. It can be a valuable aid to finding truth.

But first, we must distinguish between using noise to detect manipulation and image forensics. For instance, the June, 2008, issue of Scientific American featured an amazing article on Digital Image Forensics. However, that was more oriented toward detecting deliberately falsified photos such as adding or subtracting people from a scene. Even if an expert does the image manipulation, the present state of the art is that other experts can detect enhanced images. That is the stuff of spy stories, but what about us common folk? Can we do some simple tests on photos without investing the time to become experts?

Yes, we can. There are many ways to detect simple changes. Ron presented one. Several methods of detection rely on the inherent noise in an image. In general, noise will be different in areas where modification has taken place — almost any type of modification. So one method is to introduce a slight bit of uniform noise to a copy of an image and then subtract the doctored image from the original. The difference image will likely show a dim version of the original with edges more pronounced. (A problem to consider: Why should the difference image show edges preferentially? Hint: Think about noise.) Here’s a good example of this technique applied to a real image. The site shows an image of a woman, but when you hover your cursor over the natural image, it changes to the difference image, and the areas that have been modified stand out.

For those who want to pursue the simple, but effective, method further, there is a tutorial available here.

While the Scientific American article discussed more in depth of how to separate out the original parts for added or modified parts, either the method Ron talked about of this error method will answer the more general question of whether an image has been enhanced or not.

Why should we care if an image has been doctored? If there is no intent to deceive or break the law, then is taking a few pounds off a person’s waist so bad? Clearing up acne from a teenager is more likely kindness than harm. How does this differ from a photographer composing a scene? Is putting makeup on a model’s face via digital manipulation different from putting makeup on before the shot?

What about other types of images? The biggest image we can think of is the universe itself. Analysis of microwave background noise from the cosmos was an important confirmation of the Big Bang theory. Radiation noise left over from the Big Bang was predicted to have a certain temperature, and when the background noise was investigated, it matched the predictions. In a sense, this is the same process as detecting manipulation in a photo. Also, in the same sense, we can look more carefully at the microwave background noise. By studying the speckles in this noisy image, one can determine the dynamics of the Big Bang in the first trillionth of a second or so (actually much smaller than that). That is, by looking at minute fluctuations in the cosmic background radiation at the greatest distances that can be seen, some of the dynamics at the beginning of everything can be decoded. Noise is not always bad.

Another unexpected use of noise is to increase the sensitivity of various types of detectors. Classical astronomers quickly learned to expose their photographic plates to a faint light before using them to see dim objects in the heavens. So you might be surprised to know that everything you sense might be improved by noise. Audio, visual, and tactile response can all be improved with noise. Formal studies call this by the fancy name of stochastic resonance, but it boils down to the same thing. If you are listening for extremely faint sounds, your threshold for detection can be lowered if you also have some background noise in addition to the desired signal. This non-intuitive result is due to non-linearity in the sensitivity of the various detectors. If enough readers are interested in this subject, I can pursue it further with some specific examples. The noise can lift the detector out of an operating region where it has low sensitivity to a generally linear operating range. Obviously the stimulating noise must be low-power. Completely exposing a photographic plate ruins it for anything else, and a loud rock band interferes with normal conversations.

The main point of this post is to enumerate some of the ways in which noise can be a benefit.

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