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Pretty simple question - I am trying to figure out what exactly is different between 'de-noising' a signal, and simply filtering it (as we commonly know) to remove noise. Is this a case of lexical overlap or is there something fundamentally different? Why is it called 'de-noising'?

Edit: Perhaps crucially, when we talk of filtering a signal to maximize its SNR, we usually mean AWGN in the colloquial context. So is the 'noise' being referred to in de-noising also AWGN, and if so, is de-noising simply a different way of removing it, or is it a different type of noise (non-gaussian, colored, etc) to begin with?

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    $\begingroup$ It might be useful to point out places where you've seen references to "denoising" that is not accomplished by filtering. I think this is really just a small semantic difference: "denoising" just refers to removing noise from a signal, which could be accomplished in other ways than linear filtering (example: if you had a sample of the noise, you could directly subtract it from the signal of interest). $\endgroup$
    – Jason R
    Dec 2, 2011 at 19:48
  • $\begingroup$ @JasonR I cant really pull up those sources since I remember them in my mind as I have seen them over time in various literatures, (I seem to remember seeing it more in audio/video papers though). But one thing you said does hook into my question well - in that, you mentioned that if we have a sample of the noise, we can subtract it. This is a big part of my question on the subject - namely, if this source is random, then how can we even possess a sample of a noise vector to begin with? $\endgroup$
    – Spacey
    Dec 2, 2011 at 21:02
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    $\begingroup$ What's important is being able to discriminate signal from noise; just because noise is random doesn't mean that separate samples can't be correlated. If you have two inputs, one containing signal plus noise and the other noise only, and the noise in the two inputs is correlated, then you can use that correlation to effectively cancel some of the noise from the first input, improving your SNR. It should be said that this would be a pretty rare set of circumstances, though. $\endgroup$
    – Jason R
    Dec 2, 2011 at 21:09

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De-noising is about the goal, and filtering is about the technique you employ.

You can obviously de-noise via filtering. For example, if you know that your system cannot transmit frequencies above a certain threshold, you can apply a low-pass filter. However, you can de-noise by other techniques as well, such as by averaging multiple recordings of a signal. Similarly, you can apply filters with other goals than (just) noise reduction.

Note that "noise" may not necessarily be additive random noise - depending on your context, non-pertinent signals may be lumped with noise as well, such as the sound of vuvuzelas.

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  • $\begingroup$ "Note that "noise" may not necessarily be additive random noise - depending on your context, non-pertinent signals may be lumped with noise as well, such as the sound of vuvuzelas." Yes, this is what I have come to learn/believe. The term 'de-noising' is very general, the term 'noise' in the phrase confused me because one automatically starts to think of AWGN at the very least. I understand now it can mean any think that is 'unwanted' in the signal, white, colored, random, or correlated. Or vuvuzelas. God theyre so annoying. :-) $\endgroup$
    – Spacey
    Dec 5, 2011 at 18:26
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Just as a for instance, de-clicking might be considered a part of a de-noising system. Removing clicks comes up in digitizing vinyl audio records - dust that cannot be removed without damaging the substrate can cause an audible click in the digitized audio signal. There are systems that can detect and remove these clicks that use model based estimators to predict the samples that are masked by a click. Linear filters are often used in such systems, but are not sufficient to fully accomplish the masking.

The algorithms run along the lines of, high-pass filter, square and low-pass for an energy detector, find places where high frequencies attack and decay very quickly, fill in those samples with some estimator.

Median filters are another example of noise reduction through something other than a traditional linear filter.

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  • $\begingroup$ @DilipSarwate - I guess those could be considered the analog, uh, analogs? to digital de-clicking. $\endgroup$
    – mtrw
    Dec 4, 2011 at 16:36
  • $\begingroup$ @mtrw Nice answer ... never heard of those so called non-linear median filters... will have to learn about them at some point. Meh. The more I learn things I know now, the more I find out the extent of those which I dont know. :-/ $\endgroup$
    – Spacey
    Dec 5, 2011 at 18:20

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