Fixing the shape of small punctate objects (stars)?

[pipet]

I recently took some photos of the night sky in a nice dark location. Astrophotography is not my forte, but some shots came out fairly decent, but when zooming in on the picture below, the stars - especially in the corners - have this weird shape with those trailing edges. I was wondering, if there is a filter operation (e.g. some combination of luminance masking and a blur filter) that would be able to round out these objects?

  

[thomaso]

I would try blurring the stars to change their U shapes to O shapes, e.g. Diffuse Glow …

... and, to protect brightness levels, maybe first a Gaussian Blur + reduced layer opacity (e.g. 50%) for the Diffuse Glow, + increasing vibrance/saturation (50/100) to restore colours (before or after), for example:

[pipet]

Great - thanks!

Now, is there a way to shrink these a bit?

[Ldina]

One approach:  try a Live Minimum Blur filter and mask it to the areas you want to "shrink". 

[thomaso]

1 hour ago, Ldina said:

 try a Live Minimum Blur filter and mask it to the areas you want to "shrink". 

… and you may try the “Circular” option in this filter.

Also the settings in the "Diffuse Glow" filter affect the star sizes (e.g. Radius, Threshold)