A Gaussian distributed noise is commonly used to simulate TOA sensor radiance. Yet some references (e.g. S. Cogliati 2015, W. Verheof 2014) said that the variance of the noise was linearly related to the TOA radiance. What does this mean?
The Gaussian distribution is a two-parameter distribution, where the parameters are the mean and the variance, which are entirely independent of each other. In other words, increasing the mean noise does nothing to the variance. The variance stays the same.
To say that the variance of the noise is linearly related to the TOA radiance indicates that the Gaussian distribution does not apply, because the variance is a function of the mean and not independent of the mean.
The Rayleigh distribution is a single-parameter distribution, so that its mean and variance are related. The variance is proportion to the square of the mean. If the TOA radiance is the square of the mean of the noise distribution (I do not know if this is true), then Rayleigh distributed noise would have the property in question. That is, the variance would be proportional to the TOA.
In any case, the meaning is that, unlike the Gaussian distribution, the variance and the mean are related in actual noise statistics.
Ronald
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