jpeg with grinded edges that needs smoothing, how to?

I got an image of an charicature and the edges are a bit griny or jagged so to speak.

What would be the best way to smoothen this out?

I don't want to use gaussian blur.

You may have to go through segment by segment but I would give the median filter a try. If there is anything intricate you will have to retouch those spots.

Keep the original in another layer at all times as you may need to move it on top and use the color layer effect for adding the color back in.

Would you be able to post a sample section of the image at actual pixel size?

Yes sure here it is, as you can see the outline is a little jagged.

From other examples i see on the web there is a big difference those outlines are smooth and tight.
I believe this is called vector art?

It's still not brilliant, but is an improvement.

To replicate with full image:

Image > Image Size
Increase resolution to 300dpi, ensuring bicubic resampling is on (to give filter something to work with)
Filter > Noise > Dust & Scratches (radius: 4px, threshold: 15px)

They could be, but if bitmaps are scanned/created well they'll appear sharp on screen. It may be worth contacting whoever supplied it to see if they have a better version available.

Well, with something that simple I would just trace over it. Open it up in PS, create a new layer, trace, throw the original layer away, and save as.

I think that is merely a small portion of the whole image, which probably contains lots of tonal detail.

Thanks Impel GD, the methods you described are PS methods right?

I will put that in my private tutorial folder i'm kind of indesicive when it comes to designing and i am on another tour regarding the image i wan to use for my project...but nevertheless this is very usefull information.