Two small suggestions if you have Photoshop or similar.
1. Select the blue area and reduce the noise.
2. Select the Moon and sharpen. Radius = 0.8 Amount by say 100% for starters.
When selecting the Moon, leave out the edge.
The way I do this is by drawing a lasso tool on the inner 80-85% and leaving out the outer rim of the Moon.
Then right-click and select feather and punch in a number here of say 20 (depends on the size of image you are using)
then sharper as described above.
This will sharpern the Moon with the sharpening fading out towards the edge. However, you don't want the edge sharpened at all as it will give the edge of the Moon an artificial hard white edge.
  