I think the banding is there due to jpg compression, or possibly low bit depth, but I managed to reduce the banding a bit. The lines are still there if you look closely, but the banding is less pronounced. This was done with a simple gaussian blur in Gimp. Others may be able to do a better job, but hopefully you'll find this helpful.
Do you reckon this is a bit better? I just blurred the original (which is a much easier way of doing it than however the OP's one was made).