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Old 06-03-2014, 07:58 PM
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deconvolution - long post

Thought it might be an appropriate time for some discussion on deconvolution. As a straw man to start off, the following is my understanding of the process and what it does. Sorry its a bit long winded. Regards Ray

Stars are effectively unresolved points of light with no size, but with varying intensity. The intervening atmosphere and limited optical resolution of a telescope combine to spread the points of light into balls of light with bright centres and wings of reducing brightness. The spread of the light to surrounding pixels is described by a point spread function (PSF), which generally has a bell shape similar to a 2D Gaussian function, but with more extended skirts. Brighter stars have proportionally brighter skirts, so we see them as being larger than the dimmer stars.

So, how to make an image closer to reality - ie a collection of point sources of varying brightness? The simplest way is to look for adjacent pixels with different brightness – and then increase the contrast in that region. The logic is that if there is a small brightness difference in the blurred image, there must have been a larger brightness difference in the original scene. This is the basis of all filter-based sharpening – some methods are much more complex and look for brightness variations over differing scales, but they all work by enhancing the contrast in regions of fine detail.

Deconvolution is somewhat smarter, since it attempts to do an inverse of the blurring process that damaged the image in the first place – if you know the result (the image) and what the point spread function looks like, it is (almost) possible to take out the blurring and substantially reconstruct the original scene. The atmospheric/optical blurring is a convolution process and the reverse process is called deconvolution.

The most successful deconvolution methods for astro images have been the relatively gentle Lucy-Richardson and van Cittert. For these to work, the PSF must be known. You could guess what it might be, but it is much better to measure it directly using unsaturated stars in your image - software such as PixInsight allows you to apply a measured PSF to the deconvolution. Apart from being the best way to get the true PSF, if there is any odd shape to the measured PSF (eg the stars are slightly trailed), deconvolution can compensate and not only tighten up the stars, but make them less distorted as well.

Despite the advantages, deconvolution cannot get back all the way to the original scene for many reasons, including:
1. There may not actually be a unique solution if the scene is very complex and noisy (eg if large numbers of stars are close together)
2. Noise will be amplified
3. Sensor non-linearities, errors in the PSF and sampling problems will produce artefacts that are not part of the original scene
4. Saturated stars will not be properly sharpened
5. If the scene has continuum (eg nebula), there will be regions where a star has been tightened and the donut region left behind is undefined – no nebula information was recorded in this region and there is no longer any star data.

The end result of a deconvolution process will be tighter stars with much sharper edges – you will not be able to get right back to the original scene (with point stars), but you can get some way there. The criticisms levelled against deconvolution – that it produces hard looking stars and may “make up” data that isn’t really there seem a bit harsh. Stars really are very hard edged objects (although we seem to insist on soft fuzzy ones by convention) – and a properly implemented deconvolution process cannot invent information from good data, but it can produce artefacts from noisy or non-linear data. My impression is that we now seem to be using deconvolution in a hybrid mode – able to accept it as a lightly applied sharpening tool, but drawing the line at embracing the full blast of a deconvolved image, complete with tiny saturated hard-edged stars and previously unavailable detail in extended objects. And yet that is exactly what the process is designed to achieve – and it is largely what Hubble images look like.

ref:http://www.astro.rug.nl/~peletier/signal/starck.pdf

Last edited by Shiraz; 11-03-2014 at 04:33 AM.
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Old 07-03-2014, 07:48 AM
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He he nice write up Ray, I assume this post was instigated by some of my recent comments on the validity of deconvolution?

The key here and the bit I am not sure of and questioning is how does the decon algorithm apply a PSF to the non stella detail when the PSF was measured and created from looking at a star..?

Mike
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Old 07-03-2014, 08:07 AM
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He he nice write up Ray, I assume this post was instigated by some of my recent comments on the validity of deconvolution?

The key here and the bit I am not sure of and questioning is how does the decon algorithm apply a PSF to the non stella detail when the PSF was measured and created from looking at a star..?

Mike
yuup .

the PSF applies to the whole image, not just the stars. The whole image is blurred by the atmosphere and the optics, so the whole image should be subjected to the reverse process of deconvolution.

An easy way to measure a system Point Spread is to pass light from a point source through the system and what comes out the other end is the PSF - in astro imaging, isolated non-saturated stars provide the point sources you need. Using the stars is just a convenient way to get the PSF for the imaging conditions, but once you have it, it applies to the whole image. Deconvolution is widely applied in microscopy, where there are no readily available point sources. PSF can be determined using tiny fluorescent beads to create artificial equivalents of the stars used in astronomy, but once PSF is determined using such a source, it is applied to the normal images - same thing in astronomy.

I would be most interested in your view on where deconvolution fits in. It does have wide application for technical analysis, but when used as designed, it produces results that do not fit into the "pretty pictures" mould. Maybe there can be a place in our hobby for images that extend resolution at the expense of "niceness" in the rest of the image. I think that there is a lot that can be done to move amateur images into higher resolution regimes, but suspect that there might be a fair bit of resistance to such an approach. Might be fun to try to push the boundaries a bit though. Regards Ray

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Old 07-03-2014, 08:14 AM
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the PSF applies to the whole image, not just the stars, since the whole image is blurred by the atmosphere and the optics. An easy way to measure a system PSF is to pass light from a point source through the system and what comes out the other end is the PSF - in astro imaging, isolated stars provide the point sources you need. Using the stars is just a convenient way to get the PSF, but once you have it, it applies to the whole image. Deconvolution is widely applied in microscopy, where there are no natural point sources. PSF can be determined using tiny fluorescent beads to create artificial equivalents of the stars used in astronomy, but once PSF is determined using such a source, it is applied to the normal microscope images. Regards Ray
So if we have an irregular shaped knot in a galaxy arm say (particularly if it is saturated) what does the application of the PSF derived from a star do to this shape?

Mike
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Old 07-03-2014, 08:56 AM
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Deconvolution will not change the shape of the knot (unless the system has star trailing - decon will partially correct for that), but it will enhance finer detail and increase fine noise. If anything is saturated, you get enhancement of the edges of the saturated region, but there is nothing that can be done to extract info that is not there. Ray
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Old 07-03-2014, 09:02 AM
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Originally Posted by Shiraz View Post
Deconvolution will not change the shape of the knot
Assuming you have collected/created a valid PSF in the first place..? I am thinking that correct and judicious application is the key here. I have seen deconed galaxy data for example that just doesn't look right and the detail features look to have just been made more like point sources

Good discussion

Mike
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Old 07-03-2014, 09:53 AM
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Originally Posted by strongmanmike View Post
Assuming you have collected/created a valid PSF in the first place..? I am thinking that correct and judicious application is the key here. I have seen deconed galaxy data for example that just doesn't look right and the detail features look to have just been made more like point sources

Good discussion

Mike
Spot on. If the PSF is not correct, the results will be wrong. Using the stars to get the PSF is the way to go - guaranteed to be the appropriate PSF if the stars are isolated and not saturated. If using deconvolution as a sharpening tool with "guessed" PSF, it is possible to really mess up an image.

Nothing you don't already know, but attached image shows effect of decon on a complex image - PSF was taken from stars. Looks to me that deconvolution is not making up detail - just peeling back a layer of blur when compared to the VLT image (of course it is nothing like as good as the VLT image, but its heading the right way). This is as far as the deconvolution could go on this image due to noise, but it may be possible to go even further with more signal (aaugh, not mega data!!) Regards Ray
Attached Thumbnails
Click for full-size image (deconcomparo.jpg)
99.3 KB165 views

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Old 07-03-2014, 10:14 AM
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Mike,

Maybe trying to think of it another way.
Its not completely scientifically correct but almost, but easy to understand !

The light from the distant source has become abberrated during its journey from source to CCD - by space, by the atmosphere in numerous ways and by our optical system.
Sufficiently so, that the light from any given infinitely small point has been spread out across the image we see.

So that means that for one pixel in your image - it is comprised of light from the original source point, plus a little bit of light from every other pixel from the original source - in varying degrees . . . and that some of the light that should have been in that pixel (representing the source detail) likewise got spread out over the rest of the image.

What deconvolution attempts to do with varying degrees of success is put all the light back into the right places !

It doesnt matter that the source is a point source (like a distant star or infinitely distant galaxy or an extended source like a nebula or nearer galaxy) the light is being abberated similarly. Its just that its just so much easier to mathematically determine (and validate) the PSF on a point source of light - but all light is affected and therefore all light sources can benefit from being corrected by deconvolution.

The result is significantly enhanced contrast and significantly enhanced detail between what we see before correction and what we would see if everything was perfect.

If the Point Spread Function for that image, that object and that optical system combined was able to be determined perfectly and that it applied equally across that image we could do a pretty good job of recovering the original data.
But of course things arent quite that simple

There are many different methods of either 1. trying to determine what sort of PSF applies, 2. what the PSF is, 3. how much simplification the algorithm has in it and what assumptions are used or 4. the many processes for applying in the reverse the effects of that PSF.
Then there are all the tweaks that each algorithm permits to try and fix up common problems and number of iterations etc
The level of mathematics employed in deconvolution are typically at the bleeding edge of maths theory.

The most successful algorithm that I have read about (from Eric) is the MCS deconvolution - the initials MCS are after the authors.

Rather than try to apply the perfect correction MCS assumes it can never do this and only tries to correct for a lesser amount, but in doing does not introduce as many artifacts and for reasons that are best read in their papers, has to date produced the most scientifically accurate deconvolution, such that true quantitative scientific use of the data after deconvolution can be performed as opposed to getting pretty pictures which may help with spatial information and resolving detail.

Here is an example of MCS
http://www.orca.ulg.ac.be/OrCA_main/...n/Deconv4.html
If you start Googling you will find lots of real life examples that replicate that example

As you say there are many examples of bad deconvolution published where some aspect of the original data is improved, but often at the expense of other features - such as ringing
That link shows some obvious problems.

Cheers

Rally
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Old 07-03-2014, 01:00 PM
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Cheers Ray and Rally, I was generally familiar with what decon did and how it worked but (still) have my reservations with its use in the general amateur astronomical community, that was all.

Having said that, both of you have managed to improve my mental picture of how it should work, so cheers for that men

Now I just need to find a good piece of Decon software to use I have never been happy with the results provided by Astroarts application of it (so very rarely use it) but I suspect I am not utilising it correctly either

Thanks again guys

Mike
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Old 07-03-2014, 02:14 PM
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Great summary, Ray. Just one thing I'd add is that a truly accurate PSF would be a complex beast varying over time and also across the imaging field. The best we can do is only a rough approximation. That might be one reason for not pushing a decon too far.

Cheers,
Rick.
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Old 07-03-2014, 02:22 PM
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Spot on. If the PSF is not correct, the results will be wrong. Using the stars to get the PSF is the way to go - guaranteed to be the appropriate PSF if the stars are isolated and not saturated. If using deconvolution as a sharpening tool with "guessed" PSF, it is possible to really mess up an image.

Nothing you don't already know, but attached image shows effect of decon on a complex image - PSF was taken from stars. Looks to me that deconvolution is not making up detail - just peeling back a layer of blur when compared to the VLT image (of course it is nothing like as good as the VLT image, but its heading the right way). This is as far as the deconvolution could go on this image due to noise, but it may be possible to go even further with more signal (aaugh, not mega data!!) Regards Ray
Hey Ray, what software do you use for your decon?

Mike
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Old 07-03-2014, 03:05 PM
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Hey Ray, what software do you use for your decon?

Mike
PixInsight. The best algorithm I have come across though is something called RL2 in IRIS, which can sharpen without much in the way of artefacts. However, since I use PI for everything else, I normally use the vanCittert algorithm in that package, with local deringing support and dynamic PSF. regards Ray
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Old 07-03-2014, 03:13 PM
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Great summary, Ray. Just one thing I'd add is that a truly accurate PSF would be a complex beast varying over time and also across the imaging field. The best we can do is only a rough approximation. That might be one reason for not pushing a decon too far.

Cheers,
Rick.
thanks Rick. Good points. I guess that an advantage of using dynamic PSF in PI to extract the PSF from the image is that you get the PSF applicable to that combined image, so time variability should not be too big an issue? PSF must be averaged across the field though, so spatial variability will still be a major problem. In any case, I understand that even slight errors in the PSF can have huge effects if the deconvolution is pushed too far - never had high enough SNR to get into that region though . regards ray

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Old 07-03-2014, 03:47 PM
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PixInsight. The best algorithm I have come across though is something called RL2 in IRIS, which can sharpen without much in the way of artefacts. However, since I use PI for everything else, I normally use the vanCittert algorithm in that package, with local deringing support and dynamic PSF. regards Ray
Pixinsight huh?....after initial resistance, many seem to eventually succumb to the magnetic power of PixInsight ...hmmm?

Cheers for that

Mike
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Old 07-03-2014, 05:17 PM
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Pixinsight huh?....after initial resistance, many seem to eventually succumb to the magnetic power of PixInsight ...hmmm?
Come join us on the dark side, Mike <sinister cackle>
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Old 07-03-2014, 05:36 PM
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Maaaaaaate I am Mr don't change anything if it is working (except the deconvolution)

Better look into it groaaaan....

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Old 07-03-2014, 06:21 PM
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My understanding is Decon works better on oversampled data -it gives the algorithim something to bite on.

I see that with Trius data from the CDK. It does take decon quite nicely without artifacts (so long as not overdone).

Like any sharpening tool easily overdone. But several layers of different decon strength is a very useful tool in bringing out galaxy data. I don't see a conflict in that its merely sharpening. Much like using unsharp mask (gasp - does anyone use that anymore??).

Greg.
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Old 07-03-2014, 09:49 PM
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Maaaaaaate I am Mr don't change anything if it is working (except the deconvolution)

Better look into it groaaaan....

Hi Mike,

I am still using CCDSharp from SBIG (c. 2002), best bang for the buck - it's free. It's a one trick pony software - it only does Lucy-Richardson. It has deringing and noise reduction (to reduce amplified bgd splotches) built-in too (but you can't control that part). Overall I think it's still the best LR implementation out there except there are no bell or whistles...
my Arp244 image from last year was improved quite a bit with CCDSharp.

But it is true that decon requires 'oversampling' or at least critical sampling to work properly. What it is doing is sacrificing/trading SNR for spatial resolution, but there needs to be enough pixels per PSF to put that increased resolution into, and of course enough SNR to barter with! Sometimes undersampled images can be upsampled (resized into a larger buffer) and then decon'ed, but I don't think it works as well as imaging at a higher pixel scale since interpolation is added artefacts that can get amplified.

Best,
EB
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Old 07-03-2014, 10:40 PM
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Hi Mike,

I am still using CCDSharp from SBIG (c. 2002), best bang for the buck - it's free. It's a one trick pony software - it only does Lucy-Richardson. It has deringing and noise reduction (to reduce amplified bgd splotches) built-in too (but you can't control that part). Overall I think it's still the best LR implementation out there except there are no bell or whistles...
my Arp244 image from last year was improved quite a bit with CCDSharp.

But it is true that decon requires 'oversampling' or at least critical sampling to work properly. What it is doing is sacrificing/trading SNR for spatial resolution, but there needs to be enough pixels per PSF to put that increased resolution into, and of course enough SNR to barter with! Sometimes undersampled images can be upsampled (resized into a larger buffer) and then decon'ed, but I don't think it works as well as imaging at a higher pixel scale since interpolation is added artefacts that can get amplified.

Best,
EB
Cheers Eric, yes I was aware that decon worked better with greater sampling. Wonder if CCD sharp would work with a Starlightxoress camera...?

Mike
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Old 07-03-2014, 11:51 PM
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Like any sharpening tool easily overdone. But several layers of different decon strength is a very useful tool in bringing out galaxy data. I don't see a conflict in that its merely sharpening. Much like using unsharp mask (gasp - does anyone use that anymore??).

Greg.
Hi Greg. Well you could use it for merely sharpening, but then you would not be using most of its capabilities.

Deconvolution is a fairly general purpose image restoration method. It certainly does help sharpen up an image with atmospheric blurring, but, used appropriately, it can also help correct for irregular star shapes, stray diffraction patterns (possibly), minor defocus, motion induced blur (eg from wind), residual aberrations etc. There is a plug-in for Astroart that can be used to correct for coma and the use of deconvolution to correct for SA in early Hubble data is well known.

An appropriate deconvolution algorithm should automatically give you close to the best possible enhancement of stars and galaxies. If it measures PSF it knows how the image has been affected and from that, tries to correct for what has actually gone on in the imaging process - without any guesswork from the user.

In addition, most of the iterative algorithms include noise reduction and deringing at each step, so you don't need to do much massaging of the enhanced image.

Typical deconvolution algorithms are much more comprehensive and potentially reliable than ad-hoc sharpening, even though they can be used in that way if desired. Regards ray

EDIT: just noticed that PI has an input to allow motion blur to be incorporated into a predefined PSF.

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