How Does Mean Centering Affect the Result of Using SVD to Compress Images?
I will try to illustrate why it is important to remove the Mean from data when doing the PCA (SVD is the tool to basically do the PCA approach to dimensionality reduction -> Compression).

If the data isn't centered you will have one (Most probably the most dominant) component (Direction) which will point to the center of the data.
Since all directions must be orthogonal, it means the next directions, which should be correlated to the data itself will have harsh constraint.

You want the directions to be chosen according to the data layout and not according to its position in space.