# NOISE MODEL explanation in detail

hi sir,
I am new to cryoSPARC. I have started to learn recently. Kindly help me understand the difference between symmetric, white, and colored noise models.? When should we impose this restriction- during ab initio or nonuniform refinement?

Hi @BhawnaMishra, is there a problem in your data analysis that you think relates to the noise model? Iâ€™ve rarely needed to touch these kinds of parameters and rarely see it discussed. E.g.,

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Hi @BhawnaMishra, and welcome to cryoEM!

To begin with, I agree with @drichman â€” we have found that the default noise models are almost always the right choice, and I wouldnâ€™t generally recommend changing them from their default values.

However, I would still be happy to to explain the difference in these noise models, and what we use noise models for generally.

## What do we mean when we say noise has a color?

We can define â€śnoiseâ€ť as a series of values with no information content. Put another way, noise is a series of random values. However, defining exactly what we mean by â€śrandomâ€ť is not as obvious as it first seems!

We can describe different types of noise (randomness) by their â€ścolorâ€ť.

An image of white noise from Wikipedia

White noise is equally noisy at all frequencies (more formally: white noise has equal power over all frequency bands). This type of noise sounds like an old untuned TV or radio, and is not so common in natural systems. It is called white noise by analogy to white light, which has an equal amount of all the visible frequencies.

An image of pink noise from Wikipedia

Colored noise has a different â€śamountâ€ť of randomness at different frequencies. For instance, pink noise has more low-frequency noise than high frequency noise. It sounds like rushing water, and is more commonly observed in natural systems.

If you compare the image of pink noise to the image of white noise, you see larger regions of the image that have the same average brightness. This is because pink noise has more variation at low frequencies than at high frequencies!

In cryoEM, we generally use a colored noise system, since we expect that our images have more noise at the higher frequencies. We also often observe a very noisy peak in the medium frequencies, the source of which we do not yet fully understand.

# What is symmetric noise?

Our images are 2D, so we need to generate 2D noise as well. However, we have no reason to expect that our images will be noisier in, say, the vertical direction than the horizontal direction. In symmetric noise we therefore enforce rotational symmetry on the noise, such that noise of a given frequency in direction A will have the same intensity (that is, the same level of â€śnoisinessâ€ť) as the same frequency in direction B.

In 2D plots of noise, this appears as rings of the same intensity, such as the right-hand side of the plot below image. However, with a symmetric noise model, we can just plot a single line from the center of this plot outward, since all such lines will have the same profile. This rotational average is whatâ€™s plotted on the left-hand side of the plot below.

# Why do we need a noise model in the first place?

You may be wondering what the noise model is used for at all â€” why do we need to know how noisy our images are, if thereâ€™s nothing we can do to remove that noise? The answer is that we can use our noise model to tell us how trustworthy our images are at a given frequency.

For instance, say our noise model tells us that the images are particularly noisy at 10 Ă… for some reason. During alignment, we can downweight the contribution of the particle images at 10 Ă…, since we know they are not particularly reliable at that frequency. This may improve the overall quality of the alignment, since weâ€™re only using frequencies weâ€™re more confident in.

I hope that answers any questions you might have, but please feel free to let me know if thereâ€™s something I didnâ€™t quite explain clearly!

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If we have more high frequency noise on average, is the noise model effectively acting as a fine-tuned low-pass filter for purposes of alignment?

Great question @ccgauvin94!

I want to first be very clear that we do not actually use the noise model to filter the particle images at any point â€” this is all just to build a mental model of what itâ€™s doing.

With that out of the way, your model is more-or-less correct! Itâ€™s not a low-pass filter per se, since there is the mid-resolution noise I mentioned earlier (i.e., the noise is not monotonically increasing), and the response is not necessarily 1.0 anywhere over the frequency domain, but that doesnâ€™t mean itâ€™s a bad mental model.

Itâ€™s probably best to think about this as a prior on the error, e.g., â€śI expect the error due to noise at frequency K to be higher than at frequency Lâ€ť. We can factor this prior into the score of a given alignment, so that an alignment with more error at frequency K is treated as a better alignment than one with the same error at frequency L. So if in this example K was always greater than L, you could certainly think of it as a tuned low-pass filter during alignment.

The most formally-correct way to think about this is that the noise model is a filter applied to the residual, i.e., the difference between the reference projection and the particle image, in Fourier space. We modulate the error values in each Fourier shell by the amount of noise in that shell before picking the best pose.

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Dear sir,
In the Noise Model, generally, the default parameter is symmetric. But when we click there it shows it can be changed to white, or colored are well depending on the data. I have tried to find the explanation for that but I was unsuccessful. But I am keen to understand them in detail. Kindly also quote a link where I can read about them. Also I would like you to put some shine on the fact that is it required to change those parameters or we should keep it default only?

Thankyou so much for your explanation sir