If some of the edges are infinitely sharp, and you know which ones they are by looking at them, as in my example, then it's using more than all its bandwidth at any resolution.
That's true in the 1D case as well. That requires upsampling with information generation before downsampling. Using priori to guess missing information is a task that will never be finished and is interesting. It isn't necessary for a satisfactory downsampling result.
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If some of the edges are infinitely sharp, and you know which ones they are by looking at them, as in my example, then it's using more than all its bandwidth at any resolution.
That's true in the 1D case as well. That requires upsampling with information generation before downsampling. Using priori to guess missing information is a task that will never be finished and is interesting. It isn't necessary for a satisfactory downsampling result.