D600 High ISO in DX

Started Nov 23, 2012 | Questions thread
Re: On noise estimation

Joofa wrote:

Leo360 wrote:

Is L2 best metric in this case?

Not necessarily. But usually the one that is most tractable mathematically. If you are a physicist then possibly it is the only thing you know. If you are an electrical engineers then you know its limitations.

As a physicist by training and an electrical engineer by occupation I greatly appreciate your humor

L2 metric is firmly tied to the Gaussian distribution where it raises naturally in log-likelihood estimation, hypothesis testing, etc. If the underlying distribution is not Gaussian it is not a natural fit but people use it anyway In Quantum Statistical Physics there is a whole apparatus based on Wick theorem to deal with non-Gaussian quantities in a sort of Gaussian way with enhancements.

Furthermore it offers some intuitive justifications like for e.g., thinking that given a bunch of numbers the noise estimate is the standard deviation. So standard deviation will not be our noise estimate if our metric is not quadratic (L2).

How about alternatives like L1. In this case the optimum L1 estimator will be conditional median.

Usually L1 is better for stuff such as outlier effect, etc. But, is more difficult to treat analytically many times. Usually results in iterative optimization, instead of "quick shot" analytical solutions offered by L2.

L1 is more difficult to treat analytically but numerically it is still tractable (given moderate number of dimensions).

|| Another possibility would be MAP estimator.

| Not always a good choice. Can offer a large number of solutions.

Well, it really depends on the problem. In seriously multi-dimensional case even if the physics of the problem dictates a single global maximum finding it in the sea of local maxima could be intractable in practice.

Of course, L1, L2 and MAP do coincide and give the same results with certain assumptions such as symmetric pdfs and uniform prior.

Unfortunately, conditional probability distributions tend to break this symmetry.

Which metric is favored by human eye perception?

L1 has better immunity to visual phenomenon such as ringing, etc., in filtering problems. I would tend to think that L1 (or something between L1 and L2) would have more desirable qualities than L2 for human visual perception. But it is not easy to work with L1 all of the times.

Fully agreed!

Leo

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