D600 High ISO in DX

Started Nov 23, 2012 | Questions thread
Leo360 Senior Member • Posts: 1,141
Re: On noise estimation

Joofa wrote:

bobn2 wrote:

Joofa wrote:


bobn2 wrote:
  • the number of photoelectrons generated for a given number of photons impinged upon a pixel is not Poisson, rather binomial.

That had not occurred to me, but I think that you are right.

Yes, that is true, the number of photoelectrons generated given a fixed number of photons impinged on a pixel is Binomial (considering only the QE) and not Poisson.

No, it gets catered for simply by multiplying the photon count by the QE.

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.

Interesting. Do you have any more detail on that?

Yes. In L2 sense the best estimator of the number of photons given the number of photoelectrons generated is the conditional expectation of the number of photons. Lets call it e1. Our other, 'usual', estimator is given as (number of photoelectrons) / QE. Lets call it e2. We shall deem mean square error (MSE) as the average value of the squared error between the actual number of photons (which we don't know) and our estimate e1 (or e2) of that number.

  • e1 is unbiased -- i.e., the average value of e1 is equal to the mean number of photons.
  • e1 is conditionally biased -- i.e., the average value of e1 is not equal to the number of photons impinged on a pixel in a particular measurement.
  • e2 is unbiased.
  • e2 in conditionally unbiased.
  • The MSE of e2 = 1 / QE x MSE of e1.

Is L2 best metric in this case? How  about alternatives like L1. In this case the optimum L1 estimator will be conditional median. Another possibility would be MAP estimator. Which metric is favored by human eye perception?

Leo

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