One can measure the effectiveness of lossy image (or audio or video, etc.) compression by asking, can an observer distinguish from the original, with greater than a certain accuracy, under certain standardized suboptimal conditions: e.g., limited light, time, viewing through haze, viewing at a distance, image in motion, reduced, blurred.
Similar idea as nearly lossless image compression.
One should not ask: here is algorithm A versus algorithm B both at 2 bpp, which is better? Because the observer might want to say, A is better here, but B is better here; they are incomparable. "Better" is subjective. The only thing you can compare against is the original, and the only question you can ask is, are they the same? (Of course, the control instances are, they actually are the same.)
I think the test observer should be trained in advance to know what to look for, e.g., able to study in advance difference maps of the test images. Even the best observer can't tell the difference.
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