I don't know anything about this area of specialty, but I thought it important to point out that Huffman compression was also proven to be theoretically optimal, and then along came arithmetic compression. I only mean to say that you should be very precise about what the proof of optimality actually showed.

And, with that, I'm bracing myself to get schooled.

Edit: This reminds me of the Iterated Fractal Systems proprietary lossy image compression algorithm they tried to commercialize in the 90s. It was able to decompress to a larger scale image that introduced synthetic detail that was often convincing to the eye. Notice how this article talks about different scales.

That wasn't my point. You can do better than theoretically optimal -- indeed, their results, in many cases, do look better than sinc. Theoretically optimal makes assumptions that the source image is, in some ways, random, in a way that the real world doesn't conform to. If you know there are hard edges, you can do better.

The point is that they should be comparing to sinc. They're comparing to a known-stupid algorithm to make themselves look better than they are.