Practice question · Multiple choice
A JPEG discards most of the numbers describing an image and it still looks right. Which linear-algebra idea is being used?
Hints
- The image has the same dimension before and after. Ask what changed.
- Which basis makes 'this is mostly smooth with a few edges' cheap to say?
Show the answer
A. A change of basis, where most coefficients fall near zero
Why
Same space, different basis. Written in pixels every number is essential; written in frequencies most coefficients are near zero, so throwing them away costs little. Choosing a basis in which your data is sparse is the whole of transform compression, and the same move drives PCA and wavelets.
Practise Basis and Dimension
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