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Originally Posted by ericwbenson
Hi,
To clarify, deconvolution cannot be considered a calibration step. Calibration is the removal of known and quantifiable system artefacts. Decon of atmospheric effects is never known apriori nor easily quantifiable. The problem of decon is an inverse problem with no single nor sometimes obvious solution.
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Two points here:
1) Noise may be quantified but only by estimating a distribution. You cannot know the exact noise term in each pixel and remove it perfectly leaving only a perfect image.
2) As I already mentioned in an earlier post, you cannot model right across the whole changing wavefront of the sky, so some approximation is always to be expected. This is no different from estimating the dark noise, bias noise, amplification noise or shot noise for any given pixel.
Quote:
Originally Posted by ericwbenson
Also decon should not be applied to single subs (unless you have only one sub!). As I mentioned in a previous post above, decon is basically a trade off of high SNR (because you have more than you need and can always collect more signal with more time) to spatial resolution which you cannot easily get more of even if you collect for ever at that location.
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I've never seen this written before and I think it's not strictly true. Wikipedia states the following:
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Originally Posted by http://en.wikipedia.org/wiki/Deconvolution
In this case ε is noise that has entered our recorded signal. If we assume that a noisy signal or image is noiseless when we try to make a statistical estimate of g, our estimate will be incorrect. In turn, our estimate of ƒ will also be incorrect. The lower the signal-to-noise ratio, the worse our estimate of the deconvolved signal will be. That is the reason why inverse filtering the signal is usually not a good solution. However, if we have at least some knowledge of the type of noise in the data (for example, white noise), we may be able to improve the estimate of ƒ through techniques such as Wiener deconvolution.
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This says that deconvolution will always be limited by SNR but it is NOT a trade-off. You imply with your statement that "you can always improve SNR" that the possibilities of decon are endless and that you could somehow achieve better resolution than half the wavelength of the light you are looking at - you can't. You can restore to this point, and the question of what can be resolved varies by empirical measure (Dawes, Rayleigh, etc), but you can't beat it, ever.
NB. There are tricks to doing so in microscopy - so called Super Resolution Microscopy - but these are actually methods of isolating what are effectively point sources and using these to reconstruct a whole image, they are not part of this discussion.