The whole question of lens sharpness...

Started Jun 12, 2013 | Discussions thread
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 Re: The whole question of lens sharpness... In reply to Alphoid, Jun 24, 2013

Alphoid wrote:

For the purposes of this discussion, for signal/image/audio processing, my expertise goes well beyond everything we've talked about.

Well, you obviously have some expertise, which is why I found it so confusing that some terms and examples I was using seemed unfamiliar to you. I was looking for some common "language" in which we could communicate.

I can make statements with very high levels of confidence there. I have a basic level of knowledge about thermodynamics ... I have a deep understanding of concepts like entropy, but I do not have the applied experience of e.g. a numerically trying to invert the heat equation.

You don't need to try inverting numerically at all. You just need to look carefully at the analytic solution and see that the Fourier integral blows up for negative time. You can see the exact same behavior (and I know that you're familiar with this) with solutions to the deconvolution problem.

Also keep in mind that all along what I have been objecting to is your claim that lens blur can, in theory, be undone perfectly.

You can assume a level of knowledge about information theory somewhere in between the two, and sufficient for this discussion (I'd actually love to see you try to make the information theory entropy argument you alluded to; I believe I could take that one apart).

My thoughts re: information entropy were pretty trivial, so I'll hold off on them for the time being. If you want to discuss them in detail, we can continue this via private discussion.

Yourself?

"Sufficient."

The level of 'blur' caused by solving forward a heat equation is much greater than you would find in any sane optical system.

You can make the heat diffusion arbitrarily "small" by choosing a smaller time t > 0, and it doesn't really affect the blowup of high modes as mentioned above.

The image deconvolution problem is not ill-posed. It becomes ill-posed in a few circumstances:

• Unknown PSF (blind de-convolution)
• Extreme levels of blur (band-limited PSF, zeros in the PSF, or nearly band-limited).

Ill-posed has to do with the fundamental behavior of the system, not so much our knowledge about the PSF.

In addition, it becomes impractical if there are high levels of noise, either from the sensor or from quantization. Here, the proper term isn't 'ill-posed,' but that's a technicality.

Actually, "ill-posed" is the technical term here.

If you give me a image taken with a modern camera sensor and a modern lens at ISO100, you will not have too much noise or quantization, and the level of blur will not be such that you are just missing information.

You are missing information. That's inevitable. With increasing wavenumber your signal to noise is decreasing, conditional entropy is increasing, hence you are receiving progressively less actual information. (There, that's one of my information entropy arguments).

If you give me an image where you're trying to correct for unknown atmospheric blur, or a \$37 million space telescope with an incorrectly ground lens, a Holga, or an ISO6400 image, all bets are off. That's where the research papers kick in that talk about ill-posed problems, and much fancier algorithms.

The research papers usually start off by mentioning how the problem is well-known to be ill-posed, and then goes on to describe how the authors plan to make a go of it anyway.

You were about to get to how entropy fit in.... I'm still waiting. So far, the best I've gotten is to use it as a fancy word to mean 'time.'

There was the heat equation example, which you don't seem to follow/acept. Then there is the conditional entropy argument. And one more, but this is already getting too long, so it'll have to wait for later.

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