Re: Digicams With MF Film Quality

Philip Homburg wrote:
In article <1141056366.978593@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
acl <spamtrap@xxxxxxxxxxx> wrote:
Maybe I'm being stupid here, but please bear with me. Take the incoming signal to be s(x,y), that is, the number of photons at (x,y) is s. Now write s=n+\eta, where \eta is a random function such that the average <\eta>=0 and <\eta(x,y)\eta(x',y')>=\delta(x-y)*R^2; in your case, R=sqrt(n). All this means is that the signal has a random component (the noise here, \eta, is gaussian instead of poissonian, but never mind, this can be fixed but is irrelevant for my question). Now, any operation on this signal can be modelled as a mapping f(s). Well, since I already wrote s=n+\eta, it's impossible for any such mapping to be linear in n but not in the noise \eta. So, what am I missing?

You are right, I was sloppy.

(I'm not sure that understand your notation. It looks like you assume that
noise follows a Gaussian distribution in space. But the Poisson distribution
on photon noise is in time.)
No, you understood it correctly, I was just referring to the signal integrated over some time period (ie what you'd get after an exposure), and implicitly invoked the central limit theorem (I'm a physicist, therfore sloppy by definition). Don't take the expressions I wrote seriously. The only thing I wanted to express is that we can model the situation as signal+noise, so I don't see how any mapping can be linear in one but nonlinear in the other.

Now, with sufficient amounts of math it is probably possible to create an
operator such a Poisson distribution together with that operator forms an
additive group.

the sum of several Poisson-distributed variables is also Poisson-distributed (think of the characteristic function). I don't think that's what you meant, though.

Typically we analyze linear systems using complex numbers, so you have to
create a group that has all the properties of complex numbers as well.

Hmm, thinking about it a bit more, it is possible that the whole thing is
not as complex as it seems. Maybe photon noise does not actually play an
important role if the reconstruction algorithm is stable enough.


It seems that I am really misunderstanding the whole discussion here. Assume we know how a Dirac delta function gets imaged (ie we know the spatial frequency response); we also know everything is convoluted with this function in the final image. So we invert this process, and this is also linear. So where is the problem? Unless writing signal+noise is not a good idea.
.

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