= Lossy compression
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<Lossy compression> reduces a representation while permitting irreversible changes to the original. The encoder can map distinct <inputs> to the same <output>, so its decoder cannot recover both originals exactly. The useful question becomes how much storage is saved for an acceptable amount of distortion: <mean squared error> is one numerical criterion, but it does not by itself measure how noticeable a visual change is.
For example, storing the <arithmetic mean> of four <grayscale> <pixels> retains their average shade while discarding their arrangement. Blocks $\left(\begin{smallmatrix}0&100\\100&0\end{smallmatrix}\right)$ and $\left(\begin{smallmatrix}50&50\\50&50\end{smallmatrix}\right)$ both produce 50. The former has detail and the latter is uniform, yet the decoder receives the same value. <Lossy block averaging> makes this ambiguity, its <bit> saving and its <mean squared error> exact.
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