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