Image cleaning - How to remove line art from a colored image?
I have a couple of solutions, but I have not test either of them for you image.

I. Use simple neighrest neighber interpolation, i.e.


sweep through whole pixels,
Check if the ith pixel is black (threshold it, or get its HSV transform,
whatever)
if it's black, substitute colour values of its nearest non-black
neighborer, in the pixel.


II. Using Medial filter,

Simple apply a medial filter on the image, but do not count black pixels when applying on each window of image.