Is there a better way to "smooth out" CMYK halftones other than just blurring?

Question

I'm trying to get the best possible scan of a CD cover (although this would apply to any print media using CMYK halftoning).
With the highest setting on my scanner (3200dpi) I quickly run into the DPI of the print itself.
Here's a small portion for an example:

I can certainly blur the image, but there doesn't seem to be a good compromise for the blur radius between still having some grid artifacts and loosing too much detail. This is my best attempt:

Is there a better way to do this? Surely there's some filter that has more "knowledge" about halftones and can make a better result because of it.
The bluring above was done in GIMP, and while I'd love a GIMP solution, I'd appreciate any tool that can get the job done.

David Rouse · Answer

Please note - it has been a while since I've worked with this kind of scanning.
I think the repeating pattern (especially visible in the wood section of the image after blurring) can be caused by interference between the the scanner's grid of pixels and the grids used in the CMYK halftone screens. The traditional way to reduce the effect would be to try rotating the CD cover on the flatbed (maybe try 15, 33 and 45 degrees) and seeing if that helps the end result (after gaussian blur). You might also want to downsize the image after the blur to try and restore sharpness and reduce the visibility of any halftone dots.
Also - looking at the R, G, B channels separately the amount of blurring seems different with each one. Using your sample pre-blur image I was able to get pretty good results by using different blur settings for each channel.

Is there a better way to "smooth out" CMYK halftones other than just blurring?

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