OK, DM. You don't like my answer. You want some thing that cleaves desired from undesired. Got it. What is your answer to the question you originally posed?
The problem is that we want to divide anything into two baskets: Noise and signal.
In reality we have 4 baskets:
- Noise
- Signal
- Unwanted signal
- Wanted noise.
As the definition of what goes into the two latter baskets will depend on context and sometimes personal taste, it is a lost cause trying to make clear definitions.
Veeeeeeery interesting. How can "unwanted" as well as "wanted" signals simultaneously exist ?
Some people regard photon shot noise as signal, since it actually is part of the signal that a sensor pixel receives. Some other people define the light as a part of the measuring device which makes the photon shot noise into noise instead.
If we go with the former definition, where photon shot noise is signal, it will still be unwanted signal to most of us. So a sensor pixel will receive a combination of wanted signal - the average number of photons supposed to hit the pixel during exposure - and unwanted signal - photon shot noise.
I agree with this. I suggested that the idea of "accepted as signal" might be essential to the idea of noise. This still allows for downstream processing (perhaps by a separate subsystem) in which the components of "noise" are identified explicitly as such. At some point, there has to be a subsystem (e.g., a processing subsystem, or even the human subject) that is able to make the distinction. But at first, there would be no such distinction.
So you cannot have an Objective Definition of "Noise" because "Noise" is Subjective. ;-)
Well, human visual perception of "noise" is surely subjective - but we already knew that was true ...
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What is referred to as "noise" (at least in an ample plenty of cases in electronic engineering industry publishings) has quite evidently (in actual use by electonic engineers) extended beyond (only) random components, and has also included periodic components as being referred to as "noise".
I imagine that perhaps few viewers would argue that periodic "noise" appearing within images when they are viewed can indeed certainly be considered to be a perceptually undesirable experience.
In the making of measurements (as opposed to modelling using mathematical identities), the only way that such periodic "noise" could
not (also) be a component existing within measurement data would result from precise (spatial-domain) subtraction of those periodic components of the image-data. Seems like recording an additional "dark-frame" is the way to go if attempting that. "After that fact" methods sound (at best) tedious and problematic to implement and accomplish.
If frequency-domain post-subtraction of the same periodic components were to be used, it seems that phase-information would have to be retained and utilized in any such processes involved.
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I think that the
actual truth in measurement practices is that whenever (not dark-frame subtracted) measurements (as opposed to mathematical modelling) are involved, both periodic as well as random "noise" (intended to equate to, albeit subjectively perceived, "undesirable") components are present (with, our without, any image-sensor illumination taking place whatsoever in testing procedures).
It is the case whenever making measurements that the "total, composite image-data" (including periodic as well as random "noise") that can be measured are
Signal added to Noise.
For DxO Lab's definition of their "Signal/Noise Ratio" DxOMark data found here:
http://www.dxomark.com/About/In-depth-measurements/Measurements/Noise
... which is S / N ...
... to be accurate (and not a mere approximation - as would seem to be quite inappropriate in any cases of image-sensor illumination decreasing to very small amounts), it surely seems to me that data (must, necessarily) be derived from a subtraction of what can be measured divided by Noise:
( S + N ) / ( N )
... such that:
( S + N - N ) / ( N ) = S / N
I have a hard time disputing those mathematics implicit to measurement processes. Perhaps another contributor has a clearly different idea (and would also state the mathematical identies involved) ?
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Note that for it to
actually be true that DxOMark data does
not account for periodic "noise" (aka "banding") within it's measurement data, then precisely such a "dark-frame subtaction" as described above would be necessary (which would not eliminate, but could significantly attenuate, the magnitude of such periodic "noise" components). (Perhaps) just an interesting "coincidence" ? ...
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"
Signals":
"Photon shot noise" seems thought to be established as being a property of light itself since 1985 (see my previous post
here) - and is thus ineluctable. While making a rhetorical differentiation between "wanted signal" and "unwanted signal" appears to be
technically accurate - such technical "bifurcations" act at odds with the idea of the concept of the phrase "signal/noise ratio" relating to a numerical quantity representing
a "quality factor" that is meaningfully and readily relatable to the existence of something resembling a "wanted/unwanted ratio" which characterizes the actual
functional visual peceptions, albeit subjective, of viewers of images.
"Technicalities" seem only to detract from (as opposed to add to) to concepts involving metrics that endeavor to (at least statistically, based upon subjective individual visual perceptions) "couple" (as opposed to "de-couple") metrics described as "signal/noise ratios" with viewers' visual perceptions.
Not that some viewers may not "like it noisy". Easily accomplished "at, or after, after 'the fact' ".
DM ...
