# Different Types of Noise

I have a question about the identification of multiplicative noise. How can I see that it is multiplicative or additive noise in an image?

Cell segmentation in phase contrast In this post you pointed out that it is multiplicative noise.

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Hello Tim-Oliver,

From the reference I posted:

Distortions to the observed image are modeled by a linear inten-
sity gain function v and an additive term z; I0 (x) = I(x)v(x) + z(x),
where I0 (x) is the intensity observed at location x. The intensity
gain models attenuations to the signal. An additive or
zero-light term models contributions present even if no light is
incident on the sensor, mainly camera offset and fixed-pattern
thermal noise. It is usually nearly uniform, varying by only a few
intensity values.

So basically, my (maybe naive) guess is that if the background noise is not uniform, i.e., changes from frame to frame (or slice to slice), it must be multiplicative. Otherwise it would be additive and easily removable by subtraction.

Does it make sense?

ignacio

As far as I understand it additive noise has not to be uniform. I guess uniform refers only to the noise distribution it could also be a gaussian distribution.

I know about three different types of noise:

• Impulse Noise (salt and pepper noise)
• Additive Noise (gaussian, poisson, uniform)
• Multiplicative Noise (mostly observed in radar, ultrasound images)

The only noise which should not change from frame to frame is the impulse noise, because this noise is based on some dead pixels (salt and pepper) or other hardware defects.
Additive noise is the â€śstandardâ€ť noise for light images which is normally assumed to be gaussian distributed, but poisson distribution would be more accurate but harder to model and uniform noise is simpler to model.
Multiplicative noise is based on the pixel value, this means that pixels with a low value only show small amounts of noise and pixels with high values show bigger amounts of noise.

I thought about the subtraction of the maxprojection not as a method to remove noise but more as a method to remove the background and everything else that is not moving.

I donâ€™t think that it is possible to get rid of noise just by subtraction. For Additive noise I would use a gaussian filter, for impulse noise I would use a median filter and for multiplicative noise I actually donâ€™t know what is best to use.

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I see your point, but I think in this case it is just a matter of terminology. Given the origin of the image formation, maybe I shouldnâ€™t have called it â€śbackground noiseâ€ť but followed the paper naming convention and called it gain function. That way, we could recover the â€śuncorruptedâ€ť image by the formula

where z(x) is the additive term and looks negligible in the images that Paul sent us. Thatâ€™s why I propose to divide only by v(x). Of course, this is only my appreciation based on the observation of the data we got. It could have happened that z(x) was not negligible at all compared to v(x).
Ideally, we should have as many shots/frames/tiles as possible to properly model both as Kevin does with CIDRE.

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I see your point There isnâ€™t much additive noise in the image.

But is v(x) = average-projection of the whole stack?

Not really, itâ€™s just a fast and dirty approximation

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Itâ€™s good to be specific about the difference between noise (uncertainty) and background (wrong or non-specific signal)
For Trans light images like phase contrast captured with a ccd or cmos camera here is what you get:

###Noise sources

• Read noise, digitiser noise. Gaussian shaped random noise as electrons are converted to integer pixel values.
• Photon shot noise. Poisson distributed random noise from quantum effects of photons arriving stochastically. Noise amount is the square root of the number of detected photons. Cameras cab be calibrated so you know how many photons a certain pixel value is.
• Amplifier noise- eg an emccd camera or pmt, the detected photons turn into electrons and the number of those is amplified in several steps, each step adding multiplicative Gaussian noise.
• Fixed pattern noise from hot and dead pixels and other detector artifacts. Only a small random content. Can be measured and corrected and often is already by the camera. I might call this background rather than noise because it doesnâ€™t change much.
###Background
• Camera zero-offset bias. Zero photons hitting a pixel still gives some average positive pixel value like 100 for a cooled ccd. The read noise makes smaller values than the average. Digitiser canâ€™t make negative integers, so zero is offset to a higher value. This must be measured and subtracted in most cases.
• Non-specific background. Real photons, but from the wrong thing, eg autofluorescence or scattered or reflected light.
• Non-flat Illumination field - we want same photon flux at every pixel but thatâ€™s hard to make happen. This cam be measured and fixed. Flat field correction.

Hope it helps.

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