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Is there a possibility that future tech advances may reduce or eliminate the noise when using high ISO setting, or is this noise unavoidable and inherent to all digital sensors?
If there is a theoretical limit where noise is inevitable, how close are we to that?
It's very important to realize that it is not the high ISO setting itself that results in noisy image, it's that fact that using a high ISO setting means you capture very little light.
Light is made up of photons which are randomly emitted by a lightsource. When the light levels are low or the exposure time very short then the number of photons you get will vary considerably from
Imagine you are trying to estimate the rate at which people are leaving a shopping mall. If you only have 10 seconds to count people then the result you get will vary a lot depending on exactly when you start counting, and which exit you chose. If you have 10 minutes to count people, then you will get a much more stable answer which will be similar for all exits (assuming there is no personal preference for exits) and across different 10 minute time windows (assuming there are no other factors influencing the result).
That is what is happening when you use a high ISO setting, you capture very few photons so a set of neighboring pixels covering an object of uniform colour might receive 4, 3, 4, and 5 photons each, so instead of a smooth uniform colour you get a grainy result that changes for each pixel.
This noise is called photon noise and is the dominant source of noise in high ISO images except in the shadows. Even if you had a perfect sensor that counted and faithfully reported each photon that hit the sensor you would still have a significant amount of noise in low light.
That's not to say that we have reached the limit of high ISO performance. Not quite yet any way. Pure photon noise is very fine grained is less objectionable than the clumpy pattern noise observed in high ISO photographs.
Reducing pixel cross talk, improving the electronics in general might only have a small effect in reducing noise amplitude, but a larger effect on improving noise quality.
Wikipedia has a simulation of the "perfect" sensor where photon noise is only noise source:
Click for a larger version where you can make out individual pixels. Image by Mdf some rights reserved.
k photons on average per pixel, the magnitude of the pixel noise will be sqrt(k).
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Reduce it, yes. For example, the Canon 5D Mark III is 2/3 stops better than the Canon 5D in high ISO performance, although their sensors are the same size, because it is seven years newer. Of course, past performance is not necessarily indicative of future results, but I see no reason for incremental gains not to continue to be made.
Eliminating it completely is physically impossible. When you get to an ISO in the millions, you're trying to extract data out of a few photons. Regardless of how good your technology is, the information is simply not there for you to extract.
Now, as for getting it "perfect" for all ISOs under, say, 3200, note that there isn't really a consistent standard for "perfect." You might develop some amazing new technology that reaches some theoretical bound in signal-to-noise ratio, but does that really matter when my eyes claim this pixel should be #0f3ed2, you claim it should be #0e3fd4, and the sensor thinks it's #0d3dd3?
It already happened! On film, or early digital, high ISO meant 400, on latest full frame cameras it means 6400. Problem is that each time it happens, 'High ISO' gets redefined to be even higher, or in another words, high ISO always means "so high that current tech makes it noisy". As noted by Tony, there are eventually, physical limitations as to how far it can go.
Via Hacker News, I recently came across this paper from 2008, written by physics professor Emil Martinec in his spare time apparently.
Noise, Dynamic Range and Bit Depth in Digital SLRs
He characterizes the different types of noise that are possible, and describes their relative importance.
After reading this you'll realize that it is impossible to entirely remove the various types of sensor noise. Certainly it is possible to minimize them (in various ways), but there also other design decisions that the camera/sensor manufacturer must make that may introduce other problems or trade-offs (e.g. applying offsets in the A/D converter, see Fig. 10+11)
Regarding your questions about a theoretical limit:
"The most important noise sources for typical exposures are read noise and photon shot noise."
"The inverse of the slope of the PRNU graph (see Figure 7 for an example) is an upper limit for the S/N ratio, unless PRNU is compensated for in post-processing."
This is a problem with sensors in general - from optical sensors to accelerometers and gyros. All consumer products deal with this and try to hide the noise from the user - for example, your phone is capable of sensing vibrations way below the level that causes it to take action, and there are apps which can show you that.
Any sensor capable of recording signals accurately within the area of interest will also be capable of recording signals outside the area of interest, and signals below or above the threshold of interest are generally called noise. This 'issue' is not related to optical sensors only, it's related to the physical limitations of sensing the things we are interested in.
So the answer is no - any sensor which is 'insensitive' enough to eliminate noise will also eliminate some of the signal we want, making it impossible to build non-noisy sensors.
