Meh said:
Image noise goes up with higher ISO, fact of life.
Well that's one way of looking at it.
I would prefer to look at it as the noise being reasonably constant (within limits) but the signal being reduced due to the lower light levels available when you have to use higher ISO settings. The end result is a lower signal to noise ratio (SNR) leading to a noisier image. The post-capture ISO amplification applied gets you back to the correct image brightness, but as it boosts signal and noise equally, cannot do anything to correct the already impaired SNR, hence the noise that was there all along becomes relatively more visible.
Impaired SNR is the natural result an under-exposed sensor which of course is what you get if you use an ISO setting higher than base ISO. The exposure meter may say you are not under-exposed, but that is because it is adjusted in advance to allow for the amount of post capture ISO amplification which is going to be applied later. By going above base ISO you are effectively accepting under-exposure at the sensor.
I would therefore say that high ISO noise performance is a somewhat mythical concept, as in reality the performance at any ISO setting is largely dictated by the SNR ratio at base ISO. The better this is to start with, then the better the results as you start losing signal due to low light levels.
Fred