D600 High ISO in DX

Started Nov 23, 2012 | Questions thread
Joofa Senior Member • Posts: 2,655
Re: On random processes

Leo360 wrote:

Joofa wrote:

The interesting thing to note regarding the above is that the estimate of the number of photons impinged obtained by dividing the photoelectron count by QE (something that is done many times due to lack of other information) is a relatively poor estimater, with its mean square error being 1 / QE of the mean square error of the best (L2) estimater.

Hi Joofa,

This is what I got (pardon my ASCII math)

* And as you said, comparing the variances lead to the conclusion that the stdev{naive.est}/stdev{cond.mean.est} = 1/QE and it gets really bad for small QE.


The interesting thing to note is that I used the MSE between the actual number of photons (n_ph) and its estimate derived using the number of photoelectrons collected (n_e), and you used the standard deviations of the two estimators. Both approaches showed that the 'naive' estimator performance degrades as a measure of 1 / QE in comparison to the L2 estimator. However, there is a difference between the two approaches since the quantity that we are estimating (n_ph) is not constant and varies randomly. One way to see the difference will be that suppose our estimator gives the exact and correct value for each arrival of some photons, n_ph, then MSE will be 0, while this estimator will still have a variance, which is now the variance of the incoming photons, n_ph.

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