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Deconvolution help in PixInsight

astrophotography dslr imaging
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#1 mike8888

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Posted 15 March 2017 - 11:17 PM

Still working on my Leo Triplet, as time permits, and have progressed to the deconvolution stage. I capture the Triplet with my full spectrum modded T3i. I generated my PSF image, masks, and ran the External PSF devo process on the preview box image, only to have my galaxy end up with a bluish tinge and the following error message in the process console: ** Warning: local divergence at iteration #3. Accumulated divergence: 8.637171e-04. I've attached some screen shots of the osc image, mask, post devo image, and the devo process settings. Any help would be appreciated!

 

Mike

Attached Thumbnails

  • leo tripet osc.jpg
  • leo triplet with mask applied.jpg
  • m66 post devo process.jpg
  • Screen Shot 2017-03-15 at 10.28.22 PM.png


#2 JukkaP

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Posted 16 March 2017 - 12:01 AM

-Try softening your mask a bit whit MLT. uncheck wavelets 1-4 and run MLT to mask image.

-Drop the iterations to 1

-Not sure, but should you aply the deconvolution to CIE L.

-You dont need the local star support whit galaxy images when deringing. Just find the suitable deringing treshold whit the sliders.

-Have you checked enough stars (big and small) in dynamic PSF. Your PSF image looks quite small.

-You should run backround noise reduction before deconvolution, your image is quite noisy now.

-The image itself rules how much deconvolution you can aply.

#3 darkstar3d

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Posted 16 March 2017 - 05:26 AM

Was the image still linear when this happened?


Edited by darkstar3d, 16 March 2017 - 05:27 AM.


#4 mike8888

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Posted 16 March 2017 - 10:08 PM

The image is still linear. 

 

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#5 JukkaP

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Posted 18 March 2017 - 12:16 AM

You need to strech the image first and then try deconv.

#6 darkstar3d

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Posted 18 March 2017 - 05:46 AM

No, it should be linear. I've always ran it on a synthetic luminance to apply to the rgb

#7 darkstar3d

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Posted 18 March 2017 - 06:22 AM

Should is perhaps incorrect. Just that all the info I've seen from the PI team had the data still linear.


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#8 johnpane

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Posted 18 March 2017 - 06:37 AM

I have not yet succeeded in applying deconvolution to my color DSLR images without severe color artifacts. I have tried both working directly with the RGB image and applying deconvolution to the L component only. In the latter case, I still get color artifacts when recombining. All of my tests have been on linear images, as seems to be unambiguously prescribed.

 

For example this quote from Juan Conejero:

"Of course the image is linear—a PSF fitting process and the subsequent deconvolution would make no sense at all otherwise..."

http://www.pixinsigh...1M82/index.html

 

Or, this tutorial by another author:

"It is very important to note from this very point that Deconvolution only truly works on linear images."

http://www.lightvort...ne-details.html


Edited by johnpane, 18 March 2017 - 06:41 AM.

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#9 darkstar3d

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Posted 18 March 2017 - 07:05 AM

Those color artifacts would come from your RGB. Did you activate chrominance noise reduction on the LRGBCombination tool?


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#10 Jon Rista

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Posted 19 March 2017 - 08:09 PM

You need to strech the image first and then try deconv.

This is definitely wrong. :p For deconvolution to work, you have to work on the original data, in it's linear form, with as little other processing done as possible. In my workflow, deconvolution is the first thing I do after integration, before anything else. 



#11 Jon Rista

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Posted 19 March 2017 - 08:10 PM

I have not yet succeeded in applying deconvolution to my color DSLR images without severe color artifacts. I have tried both working directly with the RGB image and applying deconvolution to the L component only. In the latter case, I still get color artifacts when recombining. All of my tests have been on linear images, as seems to be unambiguously prescribed.

 

You must normalize the color channel weights first before deconvolving RGB data. You do this with the RGBWorkingSpaces tool...just set all the channel weights to 1.0, apply to the RGB image, then deconvolve. You should find that you no longer have artifact issues once you do this.


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#12 Jon Rista

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Posted 19 March 2017 - 08:42 PM

Still working on my Leo Triplet, as time permits, and have progressed to the deconvolution stage. I capture the Triplet with my full spectrum modded T3i. I generated my PSF image, masks, and ran the External PSF devo process on the preview box image, only to have my galaxy end up with a bluish tinge and the following error message in the process console: ** Warning: local divergence at iteration #3. Accumulated divergence: 8.637171e-04. I've attached some screen shots of the osc image, mask, post devo image, and the devo process settings. Any help would be appreciated!

 

Mike

First things first, as I mentioned above. If you are trying to deconvolve a color image, the very first step you should perform (before ANYTHING else, on the pristine integration right after it comes out of ImageIntegration/BPP) is RGBWorkingSpaces with all channel weights (Luminance Coefficients) equal to 1.0. The Deconvolution process uses the coefficients. If they differ, then it'll treat each channel differently, and that usually gives rise to color artifacts.

 

OOV6qg8.jpg

 

Second, you need a GOOD PSF to properly deconvolve. A bad PSF can wreak all sorts of havoc on your image. If you do not have any real good stars in your image from which to model a PSF, then you should also try the Parametric PSF (a synthetic PSF) and fiddle with the settings until you get a reasonable approximation of your stars and reasonable results from the deconvolution.

 

Third, you are masking WAY too heavily. You've basically masked off the entirety of the image and exposed only the galaxies themselves. At the very least, you only need a light to moderate mask for deconvolution. If you are using Regularized Richardson-Lucy, you actually do not need an image mask at all...you should be using the wavelet regularization feature to configure noise scale protections that will prevent the deconvolution tool from affecting the noise in the image at all. You may need anywhere from 2-5 noise scales, maybe even more depending on the exact nature of your image. I usually use a ramp configuration, where I ramp down from the largest noise threshold on a linear scale. Here is an example from one of my recently deconvolved images:

 

IlW3W21.jpg

 

You will also need to make sure you are using the right global dark and possibly global bright settings along with a local support star mask to allow you to properly prevent dark ringing. Again this depends on the data, and it will not always be 0.01, or 0.1, it may be something quite a bit different, and at a much larger or much smaller scale. You need to fiddle with these settings to eliminate dark ringing without preventing deconvolution entirely. 

 

Finally, make sure you are deconvolving an image that can be properly deconvolved. Deconvolution works well with well-sampled or over-sampled data. It's effectiveness is diminished greatly when the data is undersampled, as you simply cannot properly model the PSF (either with DynamicPSF or with a synthetic PSF) when it hasn't been accurately represented. The image I deconvolved with the above settings was registered with Cubic B-spline, and interpolation algorithm that handily avoids registration artifacts, but which slightly softens the data as well. I drizzled the integration at 2x with a 0.85 drop shrink to enhance resolution, which so happens to improve sampling and noise characteristic as well. (Regularization needs a proper noise distribution, something that either follows a Poisson or Gaussian distribution, to be effective.) This is a comparison of the original integration vs. the drizzled and deconvolved image (after downsampling it 2x again to get it back to native camera size):

 

JjVm5kd.gif


Edited by Jon Rista, 19 March 2017 - 08:45 PM.

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#13 JukkaP

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Posted 20 March 2017 - 12:48 AM


You need to strech the image first and then try deconv.

This is definitely wrong. :p For deconvolution to work, you have to work on the original data, in it's linear form, with as little other processing done as possible. In my workflow, deconvolution is the first thing I do after integration, before anything else.

Ok. Sorry for wrong information. Thats the way I have used it. Thank you for correcting me. Never worked for me in linear stage whit dslr image. I allways do only minor deconv. whit 1 iteration.

#14 Jon Rista

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Posted 20 March 2017 - 01:39 AM

You need to strech the image first and then try deconv.

This is definitely wrong. tongue2.gif For deconvolution to work, you have to work on the original data, in it's linear form, with as little other processing done as possible. In my workflow, deconvolution is the first thing I do after integration, before anything else.


Ok. Sorry for wrong information. Thats the way I have used it. Thank you for correcting me. Never worked for me in linear stage whit dslr image. I allways do only minor deconv. whit 1 iteration.


Deconvolution is inherently an iterative process. That you could only use 1 iteration on non-linear data is fairly telling that the process wasn't quite working properly. Getting deconvolution working properly is a matter of trial and error, it takes some fiddling, for each and every image, to get all the settings right.

If you were deconvolving color data, then you just need to use RGBWorkingSpaces as I described above on the image before deconvolving. That should address any artifact issues that occur as a result if deconvolving RGB data.

#15 JukkaP

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Posted 20 March 2017 - 04:40 AM

Thank you Jon for great information. I'am learning great stuff every day from you. Nice you have the time to share your experience.

#16 johnpane

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Posted 20 March 2017 - 05:54 AM

You must normalize the color channel weights first before deconvolving RGB data. You do this with the RGBWorkingSpaces tool...just set all the channel weights to 1.0, apply to the RGB image, then deconvolve. You should find that you no longer have artifact issues once you do this.

Thanks Jon. I did do that and still could not get satisfactory results in my extensive testing one day.

 

Your sample monochrome image is a useful example of what deconvolution can accomplish, although it conflates deconvolution with resolution gain you get from Drizzle integration. Why not post the original Drizzle integration result as the first step of the comparison, to take that variable out of the equation? 

 

Do you have an example of results from deconvolving a color image, like the monochrome one you have posted?



#17 JukkaP

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Posted 20 March 2017 - 06:03 AM

I don't know if this is a good example. This is noisy image whit not so great stars. But Jon, if you have time could you show me how to deconv. this galaxy image whit more then 1 iteration. I tryed whit custom PSF to linear image and got no result. 

https://drive.google...NFFMXzJyT2d1YWc



#18 Jon Rista

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Posted 20 March 2017 - 10:49 AM

 

You must normalize the color channel weights first before deconvolving RGB data. You do this with the RGBWorkingSpaces tool...just set all the channel weights to 1.0, apply to the RGB image, then deconvolve. You should find that you no longer have artifact issues once you do this.

Thanks Jon. I did do that and still could not get satisfactory results in my extensive testing one day.

 

Your sample monochrome image is a useful example of what deconvolution can accomplish, although it conflates deconvolution with resolution gain you get from Drizzle integration. Why not post the original Drizzle integration result as the first step of the comparison, to take that variable out of the equation? 

 

Do you have an example of results from deconvolving a color image, like the monochrome one you have posted?

 

Yes, the gains in resolution are due to both drizzling and deconvolution. I can try to deconvolve the undersampled data for a comparison. One of the reasons  usually don't bother is the CBS interpolation from registration blurs the noise characteristic a bit, resulting in it becoming rather non-gaussian (at least at a pixel level), which makes regularization to protect the noise from deconv a far less effective tool. I have found that when I have to use a mask to protect the noise, my deconvolution is even less effective.

 

For visuals, this is the noise in the default integration, softened by CBS and the kernel-based integration:

 

sNxvrAF.jpg

 

This is the noise in the drizzled integration, per-pixel and gaussian:

 

2AXO3zA.jpg


Edited by Jon Rista, 20 March 2017 - 11:02 AM.


#19 Jon Rista

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Posted 20 March 2017 - 11:10 AM

I don't know if this is a good example. This is noisy image whit not so great stars. But Jon, if you have time could you show me how to deconv. this galaxy image whit more then 1 iteration. I tryed whit custom PSF to linear image and got no result. 

https://drive.google...NFFMXzJyT2d1YWc

I took a deeper look at your data. At first glance, it appears you have both some tilt and coma issues. Another thing about deconvolution is it really only works well if the stars across your field have a consistent PSF. Even if the stars are not ideally round, as long as they are consistent across the frame, that is ultimately what matters. In your case, the stars localized around the central-lower-right area are round, while throughout the rest of the field they are not. You will have to be quite selective about which stars you use to model a dynamic PSF, and even then, because of the inconsistencies, you are likely to find that deconvolution does not work all that well. You might be better off with just using MT to do star reduction, and LHE with a proper star mask to enhance galaxy detail. 



#20 johnpane

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Posted 20 March 2017 - 11:57 AM

I can try to deconvolve the undersampled data for a comparison. 

No need to do that. In your three-image comparison, just swap the drizzle integrated image (downsampled) for the undersampled image as the first in the sequence.



#21 Jon Rista

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Posted 20 March 2017 - 12:06 PM

Jukka, I gave your data a whirl. It's not ideal for deconvolution, however pushing the settings about as far as they would go, I was able to get it to deconvolve ok. It is not great, and I would recommend figuring out the tilt and coma in your optical system for sure, as once you have round stars across the field deconvolution will become easier. Anyway. These are the settings I used:

 

l1lHD4D.jpg

 

Here is the before and after:

 

7QjXFji.gif

 

To demonstrate how much getting the settings exactly right, particularly on this kind of data, is critically important. I had to fiddle with the Global Dark setting a lot, and finally got it down to 0.0050. When I did that iteration, I had fewer issues with local divergence, but I still had some:

Deconvolution: Processing preview: drizzle_integration_DBE1_ABE_clone_SHARE->Preview02
Computing CIE Y component: done
Regularized Richardson-Lucy
Iteration 1/40: done
  s=1.6903e-004 Ds=+0.0000e+000 sn=6.0560e-006 n=9.6942e-002
Iteration 2/40: done
  s=1.6882e-004 Ds=+1.2533e-003 sn=6.0608e-006 n=2.0430e-001
Iteration 3/40: done
  s=1.6240e-004 Ds=+3.9536e-002 sn=6.0583e-006 n=1.9228e-001
Iteration 4/40: done
  s=1.5893e-004 Ds=+2.1784e-002 sn=6.0614e-006 n=1.9846e-001
Iteration 5/40: done
** Warning: local divergence at iteration #5. Accumulated divergence: 3.491416e-004
  s=1.5899e-004 Ds=-3.4914e-004 sn=6.0556e-006 n=2.1678e-001
Iteration 6/40: done
  s=1.5621e-004 Ds=+1.7798e-002 sn=6.0532e-006 n=2.0389e-001
Iteration 7/40: done
  s=1.5580e-004 Ds=+2.6339e-003 sn=6.0545e-006 n=1.9397e-001
Iteration 8/40: done
  s=1.5417e-004 Ds=+1.0545e-002 sn=6.0512e-006 n=1.8884e-001
Iteration 9/40: done
** Warning: local divergence at iteration #9. Accumulated divergence: 2.314460e-004
  s=1.5421e-004 Ds=-2.3145e-004 sn=6.0519e-006 n=1.7382e-001
Iteration 10/40: done
  s=1.5288e-004 Ds=+8.6616e-003 sn=6.0517e-006 n=1.6645e-001
Iteration 11/40: done
** Warning: local divergence at iteration #11. Accumulated divergence: 2.756877e-004
  s=1.5293e-004 Ds=-2.7569e-004 sn=6.0514e-006 n=1.5772e-001
Iteration 12/40: done
  s=1.5196e-004 Ds=+6.3594e-003 sn=6.0514e-006 n=1.5393e-001
Iteration 13/40: done
** Warning: local divergence at iteration #13. Accumulated divergence: 1.207746e-004
  s=1.5198e-004 Ds=-1.2077e-004 sn=6.0524e-006 n=1.5183e-001
Iteration 14/40: done
  s=1.5124e-004 Ds=+4.8806e-003 sn=6.0523e-006 n=1.4942e-001
Iteration 15/40:  83%
<* abort *>

I knocked Global Dark down to 0.0040 after aborting here, and everything worked like a charm, no local divergence and no dark ringing issues:

Deconvolution: Processing preview: drizzle_integration_DBE1_ABE_clone_SHARE->Preview02
Computing CIE Y component: done
Regularized Richardson-Lucy
Iteration 1/40: done
  s=3.1080e-004 Ds=+0.0000e+000 sn=6.3793e-006 n=1.9489e-001
Iteration 2/40: done
  s=3.0524e-004 Ds=+1.8228e-002 sn=6.3876e-006 n=2.9913e-001
Iteration 3/40: done
  s=2.9670e-004 Ds=+2.8784e-002 sn=6.3835e-006 n=2.6360e-001
Iteration 4/40: done
  s=2.9154e-004 Ds=+1.7713e-002 sn=6.3785e-006 n=2.6799e-001
Iteration 5/40: done
  s=2.9007e-004 Ds=+5.0602e-003 sn=6.3779e-006 n=2.7951e-001
Iteration 6/40: done
  s=2.8662e-004 Ds=+1.2047e-002 sn=6.3703e-006 n=2.6492e-001
Iteration 7/40: done
  s=2.8522e-004 Ds=+4.8898e-003 sn=6.3747e-006 n=2.5480e-001
Iteration 8/40: done
  s=2.8313e-004 Ds=+7.3767e-003 sn=6.3701e-006 n=2.5362e-001
Iteration 9/40: done
  s=2.8235e-004 Ds=+2.7662e-003 sn=6.3715e-006 n=2.4472e-001
Iteration 10/40: done
  s=2.8093e-004 Ds=+5.0600e-003 sn=6.3700e-006 n=2.4169e-001
Iteration 11/40: done
  s=2.8027e-004 Ds=+2.3443e-003 sn=6.3691e-006 n=2.3718e-001
Iteration 12/40: done
  s=2.7930e-004 Ds=+3.4786e-003 sn=6.3678e-006 n=2.3504e-001
Iteration 13/40: done
  s=2.7874e-004 Ds=+2.0117e-003 sn=6.3667e-006 n=2.3197e-001
Iteration 14/40: done
  s=2.7803e-004 Ds=+2.5555e-003 sn=6.3662e-006 n=2.3058e-001
Iteration 15/40: done
  s=2.7750e-004 Ds=+1.9070e-003 sn=6.3658e-006 n=2.2758e-001
Iteration 16/40: done
  s=2.7696e-004 Ds=+1.9437e-003 sn=6.3650e-006 n=2.2575e-001
Iteration 17/40: done
  s=2.7652e-004 Ds=+1.6023e-003 sn=6.3642e-006 n=2.2299e-001
Iteration 18/40: done
  s=2.7610e-004 Ds=+1.5181e-003 sn=6.3638e-006 n=2.2078e-001
Iteration 19/40: done
  s=2.7573e-004 Ds=+1.3468e-003 sn=6.3631e-006 n=2.1832e-001
Iteration 20/40: done
  s=2.7538e-004 Ds=+1.2795e-003 sn=6.3625e-006 n=2.1634e-001
Iteration 21/40: done
  s=2.7505e-004 Ds=+1.1708e-003 sn=6.3621e-006 n=2.1451e-001
Iteration 22/40: done
  s=2.7468e-004 Ds=+1.3562e-003 sn=6.3620e-006 n=2.1306e-001
Iteration 23/40: done
  s=2.7431e-004 Ds=+1.3658e-003 sn=6.3615e-006 n=2.1181e-001
Iteration 24/40: done
  s=2.7396e-004 Ds=+1.2843e-003 sn=6.3618e-006 n=2.1073e-001
Iteration 25/40: done
  s=2.7363e-004 Ds=+1.1762e-003 sn=6.3605e-006 n=2.0976e-001
Iteration 26/40: done
  s=2.7334e-004 Ds=+1.0725e-003 sn=6.3603e-006 n=2.0895e-001
Iteration 27/40: done
  s=2.7306e-004 Ds=+1.0363e-003 sn=6.3602e-006 n=2.0812e-001
Iteration 28/40: done
  s=2.7276e-004 Ds=+1.0755e-003 sn=6.3598e-006 n=2.0736e-001
Iteration 29/40: done
  s=2.7249e-004 Ds=+1.0033e-003 sn=6.3599e-006 n=2.0663e-001
Iteration 30/40: done
  s=2.7224e-004 Ds=+9.1432e-004 sn=6.3600e-006 n=2.0600e-001
Iteration 31/40: done
  s=2.7201e-004 Ds=+8.3521e-004 sn=6.3597e-006 n=2.0529e-001
Iteration 32/40: done
  s=2.7180e-004 Ds=+7.7716e-004 sn=6.3593e-006 n=2.0454e-001
Iteration 33/40: done
  s=2.7160e-004 Ds=+7.3375e-004 sn=6.3597e-006 n=2.0374e-001
Iteration 34/40: done
  s=2.7142e-004 Ds=+6.8540e-004 sn=6.3592e-006 n=2.0306e-001
Iteration 35/40: done
  s=2.7124e-004 Ds=+6.4406e-004 sn=6.3588e-006 n=2.0237e-001
Iteration 36/40: done
  s=2.7108e-004 Ds=+6.0946e-004 sn=6.3586e-006 n=2.0168e-001
Iteration 37/40: done
  s=2.7092e-004 Ds=+5.7867e-004 sn=6.3584e-006 n=2.0098e-001
Iteration 38/40: done
  s=2.7077e-004 Ds=+5.5199e-004 sn=6.3580e-006 n=2.0036e-001
Iteration 39/40: done
  s=2.7060e-004 Ds=+6.5003e-004 sn=6.3574e-006 n=1.9969e-001
Iteration 40/40: done
  s=2.7042e-004 Ds=+6.6053e-004 sn=6.3566e-006 n=1.9910e-001
Truncating samples: done
Normalizing samples:   0%
Computing extreme sample values: done
Importing CIE Y component: done
6.070 s

So, a tiny change of just -0.001 to Global Dark was enough to get me from non-working settings to working settings. I think with better data...a deeper integration along with rounder stars across the entirety of your field, would make it easier to find working settings. However, sometimes you just have to fiddle to get it working. Also note the regularization settings. I had to push those to the utter limit, as 16 is the max for noise threshold. I had to fiddle with the scaling (and even now, it's not ideal, I may need to bump up some of the protection levels even more to really keep the noise from being affected.)

 

I have also noticed that you seem to have hot pixels (or something that looks like them) in your data. It appears as though they may be dithered, but they may be low enough in standard deviation that they are not being caught by the clipping algorithm. You might want to run your RAW (before demosaicing) data through CosmeticCorrection (don't forget to check the CFA option!) to identify and eliminate as many hot pixels as you can before demosaicing, registration and integration. You want the cleanest noise profile you can get, as hot pixels or other deviant pixels can sometimes act as loci for deconvolution artifacts (and, for that matter, also as loci for artifacts with registration), and they can limit how far you can push deconvolution.


Edited by Jon Rista, 20 March 2017 - 12:16 PM.


#22 Jon Rista

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Posted 20 March 2017 - 12:28 PM

 

I can try to deconvolve the undersampled data for a comparison. 

No need to do that. In your three-image comparison, just swap the drizzle integrated image (downsampled) for the undersampled image as the first in the sequence.

 

Well, I AM trying to show the benefits of deconvolving WELL-SAMPLED data vs. undersampled data. Doing what you suggest, that eliminates the comparison I'm trying to make. I can throw in a deconvolved version of the undersampled data before the drizzled data, though, which would make the comparison more meaningful. 


Edited by Jon Rista, 20 March 2017 - 12:28 PM.


#23 JukkaP

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Posted 20 March 2017 - 01:58 PM


I don't know if this is a good example. This is noisy image whit not so great stars. But Jon, if you have time could you show me how to deconv. this galaxy image whit more then 1 iteration. I tryed whit custom PSF to linear image and got no result.
https://drive.google...NFFMXzJyT2d1YWc

I took a deeper look at your data. At first glance, it appears you have both some tilt and coma issues. Another thing about deconvolution is it really only works well if the stars across your field have a consistent PSF. Even if the stars are not ideally round, as long as they are consistent across the frame, that is ultimately what matters. In your case, the stars localized around the central-lower-right area are round, while throughout the rest of the field they are not. You will have to be quite selective about which stars you use to model a dynamic PSF, and even then, because of the inconsistencies, you are likely to find that deconvolution does not work all that well. You might be better off with just using MT to do star reduction, and LHE with a proper star mask to enhance galaxy detail.

Thanks for looking my data. I have serious problems finding the right distance for reducer/flattener. I have not been able to locate the problem. Too litle time whit the hobby.

You got the deconvolution to work. great job. I will try to fidle whit the data and learn from your example.

#24 darkstar3d

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Posted 20 March 2017 - 02:39 PM

I learn every day reading the forums. I wasn't realizing that local divergence was an indicator that raccoon eyes are on the way! Thanks


Edited by darkstar3d, 20 March 2017 - 03:46 PM.


#25 Jon Rista

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Posted 20 March 2017 - 03:07 PM

I learn everyday reading the forums. I wasn't realizing that local divergence was in indicated that raccoon eyes are on the way! Thanks

Yeah, when you start getting local divergence warnings, that means the algorithm is overreacting to, basically, itself, and you'll end up getting worsening concentric rings. Dark, bright, dark, bright... When this happens too much, you end up getting those "wormy" artifacts or even bright ringing around dark nuclei over the entire image. Deconvolution is inherently iterative, as what it's doing is reconcentrating energy...it's pulling energy that is too spread out due to the convolution by the atmosphere and optics, and concentrating it more tightly into the stars and brighter details. It does this in little steps, though, with repetitive evaluation and adjustment so that it effectively reconcentrates the right information. If there are any errors in earlier iterations, they can act as loci for further errors in later iterations, and the more those errors accumulate, the worse the errors get. This is why there is so much "error prevention" stuff in deconvolution algorithms...deringing, regularization, local star support, etc. These are all mechanisms that attempt to counteract the potential for errors in each iteration. 


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