· Telescope diameter. You will get a diffraction image for a star unless you have a telescope with infinite diameter. A diffraction image is a small disk in which most of the light is concentrated, surrounded by less luminous circles. By the way, if you have an infinite diameter scope, please tell me. I will be glad to see it.
· Optical system restrictions. Collimation deffects, comma (mainly in Newton scopes) and other problems contribute to distort our dot into ellipses or even funnier (or inconvenient, depending on how you take it) shapes.
· Object tracking. Specially if guiding is not performed and depending on the mount and the exposure time you will get an effect similar to that on shots of moving cars with a normal camera using a long exposure time.
· Seeing. This is produced by thermals in the atmosphere, light polution, normal polution and the like.
All above effects distort or transform our star into something different than a single dot. The whole image is distorted the same way. This transformation is called convolution.
Deconvolving an image is reversing the convolution as much as possible so that we obtain a dot for our already famous star.
In order to achieve this, the star image must be isolated and identified to CADET so that this big mesh is cleared. This star image is called PSF - Point Spread Function. PSF is a basic information for deconvolution.
Some deconvolution methods also attempt to minimize the noise. This is the case of Maximum Entropy Method. Others, like Richardson-Lucy Method simply deconvolve trying to get the most probable image. In this second case, some unwanted effects may show up. This is due to noise being amplified and concentrated the same way that stars are converted to a high intensity dot, thus producing artifacts.
Additional considerations:
Deconvolution must be the next step after image calibration and background substraction, before any additional image processing. Otherwise the results may be disappointing.
The results obtained with image deconvolution will greately depend on the image itself, mainly the signal-to-noise ratio. It will also depend on the selected PSF. It is recommended to select the PSF strictly following above guidelines.Also, try to define the rectangle so that the star is as centered as possible. Results will also depend on the selected background in a lower degree.
Deconvolution convergence will greatly vary from an image to another. Some of them will converge faster and others will converge slower. Sometimes final convergence cannot be achieved in practice, but most of the times acceptable results will be obtained after several iterations. In the case of a slow convergence but if displayed results are acceptable, don't hesitate in aborting the deconvolution process.
Finally, several parameters must be specified depending on the selected deconvolution method.
A detailed description of these parameters is out of the scope of these explanations. You may have additional details in statistics books and in several specialized web sites.