[berkay]

Analogy does not work here and is misleading. You cannot do much if anything with 20 most representative pixels (if there is such a thing) but you can infer highly valuable characteristics about the person. Yes, you cannot recreate the original data but what you end up is potentially much worse (sensitive/private) than the original data.

[darawk]

That's not really true, and is kind of a fundamental misunderstanding of how these things work.

[wybiral]

Unless the data is completely random it's not crazy to say that the data can be reconstructed from a reduced version.

If you have a million points that largely fall on a 3-dimensional line and you project that into 2 dimensions, you can easily recover that lost dimension with losses relative to the deviation. And that loss may not even matter depending on the kinds of data and margins of error you're working in.