How to polish my Louis Poulsen Artichoke ?  

There are plenty of copper...
There are plenty of copper polishing products available in most well stocked hardware stores.
Post a photo so we can see the condition if you want a better answer.
You can expect an argument about whether you should polish your copper, too.
*edited almost immediately to remove unnecessary flippancy.

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Aren't these coated in an acrylic lacquer? If thats degrading it would be something task to get it back to 100%

Patina is good.
Leave it alone.
Best,
Aunt Mark

Plating vs coating
vs uncoated copper: each condition calls for different measures. Tread lightly -- and if you're going on Antiques Roadshow with the piece, even original dust is apparently valued (well, not quite -- but you know what I mean).
[edited to correct the spelling of the second vs -- really !]

Here comes the Photo
Thanks all of you guys, Here comes the photo.
Can anyone teach me how to post image? Thanks.
(edited by DA - picture fixed)

Mother Mary says . . .
let it be.