Removal of coma from an image through cepstrum?

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pcl
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Removal of coma from an image through cepstrum?

Post by pcl » 2016-11-17T18:37:57-07:00

Reminder: coma is an optical aberration which typically arises from misalignment of optical components and which results in a point source producing a comet-shaped image (hence the name). Users of fast Newtonian telescopes will be all too familiar with this bane.

I have a star-field image which shows pronounced coma; I would like to estimate the PSF so the image can be restored to improve resolution and contrast. My initial attempt was to estimate the PSF as the image of an isolated star. It worked but not as well as I would like largely, I suspect, because of the noise in the estimated PSF. Rather than try to clean up the PSF, I took a look at the cepstrum of a 256x256 sample of the original containing several comatic stellar images. The result was rather interesting but I don't know how to go from the cepstrum back to a PSF.

It's well documented on Fred's page that a circular disk PSF will produce a circle in the cepstrum, the radius of which is twice the radius of the blur. Likewise, a linear PSF produces two points, the orientation and separation of which give the orientation and twice the length of the PSF. Evaluating the experimental ceptrum, identifying the ideal circle (resp. points), and computing the ideal PSF from the result is a standard technique.

The cepstrum of the comatic image contains a very clear ellipse, the major axis of which is aligned with the symmetry axis of the coma. The major and minor diameters of the ellipse must correlate with some parameters which characterize the amount of coma. Unfortunately, I haven't yet been able to work how to take an ideal elliptical cepstrum and transform it into an ideal comatic PSF. Extensive web searching has turned up only the well-known linear and defocus blurring cases.

Can anyone give me clues and / or references please? I can provide the comatic image sample if anyone wishes to experiment.

Thanks. Paul.

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fmw42
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Re: Removal of coma from an image through cepstrum?

Post by fmw42 » 2016-11-17T19:39:46-07:00

I have moved this to the more general image processing forum.

Perhaps you would provide an example image. You can upload to some place such as dropbox.com and put the url here.

A similar topic on generally deblurring with unknown PSF is at viewtopic.php?f=22&t=30775. See the reference he has found towards the end of the topic. It might shed light on ways to compute and deblur your coma PSF. Also see the references within.

You might also try Photoshop. They seem to have a deblur for camera shake. Perhaps that technique might help your case also.

You might also try blind deconvolution. See http://www.quarktet.com/Tria.html

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Re: Removal of coma from an image through cepstrum?

Post by pcl » 2016-11-18T03:07:35-07:00

fmw42 wrote:Perhaps you would provide an example image. You can upload to some place such as dropbox.com and put the url here.
The 256x256 sample is Image and the cepstrum is Image.

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Re: Removal of coma from an image through cepstrum?

Post by fmw42 » 2016-11-18T10:51:56-07:00

Have you tried deblurring with an ellipse shaped PSF whose diameter are the radii in the cepstrum? I am not sure if the orientation of the ellipse PSF image should be the same as the cepstrum or orthogonal. But you can try either way. You can try that using my script fftdeconvol

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Re: Removal of coma from an image through cepstrum?

Post by pcl » 2016-11-18T14:09:39-07:00

fmw42 wrote:Have you tried deblurring with an ellipse shaped PSF whose diameter are the radii in the cepstrum? I am not sure if the orientation of the ellipse PSF image should be the same as the cepstrum or orthogonal. But you can try either way. You can try that using my script fftdeconvol
I haven't but will give it a go. The shape might be good enough but the PSF is clearly not a flat elliptical disk --- it's markedly fainter in the north-east corner than in the south-west. Perhaps I can find a simple model for that also.

Another idea occurred recently: take one star image and use the correlation of that with the complete image to find similar stars. Then co-add all those images to form an aggregate with lower SNR than a single star image.

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Re: Removal of coma from an image through cepstrum?

Post by fmw42 » 2016-11-18T14:16:15-07:00

It looks like it has chromatic aberration also (the cyan on one side)?

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Re: Removal of coma from an image through cepstrum?

Post by pcl » 2016-11-18T14:36:46-07:00

fmw42 wrote:It looks like it has chromatic aberration also (the cyan on one side)?
Yup. That's why I tried CLEAN on all three RGB channels separately rather than converting to HSV, deconvolving the H channel, re-adding the HS to the clean H image and then back to RGB.

Thinking about it, I may have made an error in the RGB deconvolution, having located the maximum in each channel of the PSF separately and using that as the centroid of the PSF in each channel. Perhaps I should have found the centroid of the H channel and used that as the centroid of each RGB channel PSF. Something else with which to experiment. Need to be a little careful though because the image of Capella, where the cyan is especially visible, is grossly over-saturated and can't be used as an experimentally determined PSF.

Hmm. Thanks for prompting me to think more about the chromatic aberration issue. Note, I've no great interest in this star-field image per se but I am very interested in learning how to solve the general case for future images of perhaps greater scientific value. In particular, being able to perform astrometry and crude 3-band photometry of faint objects such as asteroids and variable stars. Anyone who is an amateur astronomer will recognize an arc of three somewhat faint stars below Capella (the brightest) in the posted image. The middle star is noticeably redder than its neighbours. This star is Capella C, a binary pair of red dwarf stars which are gravitationally bound to Capella.


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