4k Tri-Sensor... Epic?

[Daniel Browning]

Thanks again. Do you consider resolution to be a part of "signal"? So that a four-fold reduction in resolution, though it reduces noise by half (depending on the resampling algorithm), reduces the resolution four-fold, so there is less noise but also less "signal"? If yes, then I agree, although I haven't heard of that definition of SNR before. If no, and it has nothing to do with what you're saying, then I'm afraid I still don't understand.

 

[Dj Joofa]

Thanks again. Do you consider resolution to be a part of "signal"? So that a four-fold reduction in resolution, though it reduces noise by half (depending on the resampling algorithm), reduces the resolution four-fold, so there is less noise but also less "signal"? If yes, then I agree, although I haven't heard of that definition of SNR before. If no, and it has nothing to do with what you're saying, then I'm afraid I still don't understand.

You are welcome Daniel.

Firstly, the scenario normally quoted where SNR varies as some relation of the square root of the pixel size is valid only if neighboring pixels have a fixed value, but are corrupted by different amount of noise resulting with some assumptions on the noise process. Since, the signal is not constant in its neighborhood in general, even without noise, the result is approximately valid. Secondly, this scenario will correspond to simple averaging, which does not have good data smoothing properties of good downsampling.

Some sort of data smoothing is needed in downsampling to avoid aliasing due to expansion of signal spectrum after downsampling. So indeed, yes the signal degradation due to blurring inherent in data smoothing is part of SNR estimation.

As I mentioned in earlier message that some parameters are heuristically chosen. There is always an implied assumption that noise is small. But how small? Not many bother to do an analysis.

As an example, for the simple case of averaging pixels, if the smoothed signal after averaging is a certain order of the window size, then it follows that the explicit formula for the calculation of window size is related to the differential rate at which signal is varying. It turns out that for optimum results, the signal degradation due to noise must equal 4 times the signal degradation due to the smoothing of the signal. Similar results could be derived for some other window types besides simple averaging.