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For digital images, noise is assumed to be additive gaussian white noise. I remember noise in images is considered as high frequency. However, from the link https://en.wikipedia.org/wiki/White_noise, it says

a random signal is considered "white noise" if it is observed to have a flat spectrum over the range of frequencies that is relevant to the context.

Does it mean frequencies of noise will extend from low frequencies to high frequencies? Why do we try to only remove high frequency component? Is human visual system not sensitive to low frequency noise?

From the same link, https://en.wikipedia.org/wiki/White_noise

In digital image processing, the pixels of a white noise image are typically arranged in a rectangular grid, and are assumed to be independent random variables with uniform probability distribution over some interval.

It reads that the pixels of a white noise image are assumed to be independent random variables with uniform probability distribution over some interval. Does it mean that one pixel and its neighbors are i.i.d?

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  • $\begingroup$ SE.DSP wishes you a happy new year 2017, with a kind reminding signal that your question or its answers may require some action (update, votes, acceptance, etc.) $\endgroup$
    – Laurent Duval
    Jan 2, 2017 at 22:54

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Yes, the noise is wide-band.

A challenge in images resides in lowering the high-frequency noise components, while preserving the local high-frequency features of the contours and the textures, where you have fewer pixels to estimate a consistent denoised value.

On low-frequency parts, the data is generally more regular or smooth, and getting rid of the noise is often performed more easily by averaging over neighboring pixels.

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  • $\begingroup$ For images, flat regions are low frequency parts and edges are high-frequency parts. However, for noise, can I distinguish low frequency components of noise from high frequency components of noise? Noise is a 2-d matrix of random variables, and is independent from each other. can I say noise at some locations is low frequency and at other locations are high frequency. For the image from the post dsp.stackexchange.com/questions/28861/…, I find some patterns in the noise. $\endgroup$
    – Jogging Song
    Feb 17, 2016 at 15:34
  • $\begingroup$ Here, note that your noise is quantized to integer values, which may affect the perception, and it is not Gaussian anymore (though close if the quantization is fine enough). So in flat areas, with band-pass filters, you can have an idea of the frequency content of the noise. $\endgroup$
    – Laurent Duval
    Feb 17, 2016 at 15:44
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In addition to @Laurent's answer, images tend to be low-pass. That is, their main frequency components tend to be in the lower end of the range. That means that the effective SNR at those lower frequencies is not as much of an issue compared with the effective SNR at higher frequencies: white noise has more effect on high frequency features than it does on low frequency features.

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    $\begingroup$ I agree most frequency components in one image are low frequency components. Why does this lead to the conclusion that the effective SNR at those lower frequencies is not as much of an issue compared with the effective SNR at higher frequencies? $\endgroup$
    – Jogging Song
    Feb 17, 2016 at 15:38
  • $\begingroup$ @Peter K. I agree for usual so-called natural images. Seismic images however are more bandpass (in the vertical direction), and textural images may have various spectra. $\endgroup$
    – Laurent Duval
    Feb 17, 2016 at 15:41

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