The easies way to do it would be to first put the background on a background layer, then copy the logo onto 3 or 4 other layers.
Make each layer a little transparent, 10-40% should be ok.
GO in on each layer, and take the fill tool, have it fill with an anti-alias and enough so that when you fill the blank space of the layer, it eats away at the edges of the logo slightly.
Fill, then select with the magic seletor... magic wand thingy... and delete your fill, do that once on the first duplicate layer from the background.
twice on the next one up, and 3 time on the next, and so forth, make sure you set the top logo layer to 100% transparency so you can't see through it.
This should give you a good antialias.
These are a before and after... I used photoshop, but the tools should all be there in some form.
this is only 3 logo layers... if you do about 5 and use a lower transparency on the lower logo layers, it will look better.
Make each layer a little transparent, 10-40% should be ok.
GO in on each layer, and take the fill tool, have it fill with an anti-alias and enough so that when you fill the blank space of the layer, it eats away at the edges of the logo slightly.
Fill, then select with the magic seletor... magic wand thingy... and delete your fill, do that once on the first duplicate layer from the background.
twice on the next one up, and 3 time on the next, and so forth, make sure you set the top logo layer to 100% transparency so you can't see through it.
This should give you a good antialias.
These are a before and after... I used photoshop, but the tools should all be there in some form.
this is only 3 logo layers... if you do about 5 and use a lower transparency on the lower logo layers, it will look better.