From what I can see you're both looking at the same 'object' from different angles, no you can't increase the information without a better source but you can present that information better (filtering etc.) and that's what we're doing when we filter our captured video, presenting the video in a visually better way than it currently stands (the laserdisc and the plain capture).

As for the sine wave thing, the edge-directed resampler filter I'm using for VirtualDub is along the same lines, it doubles the image size by looking at the edges rather than blindly scaling the image, the results on hard edges is noticable when compared to Lanczos3 for example, sure it's not increasing the information but it's presenting it in a new (and what I feel to be a better) way.