Deliberate corruption is still corruption. As for your comparison to MPEG audio, I feel that's symptomatic - high-frequency components are perceptually negligible in audio, but stand out in video (until the stroboscopic effect). You wouldn't want to use the same encoder for both.
The Gibbs effect is absolutely due to discontinuities not being gracefully handled by a Fourier transform. Luckily point samples from a continuous function don't have to worry about that like a fully defined discrete function might, which is why I expect people want to define pixels as the former.
The Gibbs effect is absolutely due to discontinuities not being gracefully handled by a Fourier transform. Luckily point samples from a continuous function don't have to worry about that like a fully defined discrete function might, which is why I expect people want to define pixels as the former.