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Whether downsampling increases the SNR depends on the signal and noise characteristics. If signal and noise have the same spectrum, it does not. In a digital image, however, the signal spectrum falls off towards the Nyquist frequency of the sensor whereas the noise spectrum is whitish. In that case the lowpass filter associated with the downsampling operation filters out more noise than signal, and hence the SNR increases. (This is another way of formulating what you wrote.) One can just apply a lowpass filter without any downsampling, with the same result.
It brings up an interesting discussion. As far as...Show more →
this approaching my field now if image is band limited signal, down sampling will improve SNR, if it is not, down sampling will introduce alias, I am not sure this will really help with image. I think it is fair to say most case in real world shooting, it is beneficial.
However, one thing I am not so sure is camera shaking effect, as 4 blur pixel can make up one sharp one? I feel i can get sharper image easier with 12M than 36M down sized. But since this can not be scientifically verified, it is may not a fact.
The thing of this topic is really depend on your priority of photography. If you are trying to achieve fidenlity, I see no reason you don't want pixel. Consider DR is so high at base ISO even with high pixel density. For me, I don't feel the need of this. A 6M interesting foto have a lot more value than 80M non interested one. I never feel 80M interesting photo really add more value to, say a 12M.
But that is just me.