Basically this expresses the image as an image where each row is a linear combination of a set of K rows, with different coefficients for each row (or equivalently for columns).
In general it doesn't make sense to compress images this way, since the algorithm is not invariant with respect to 2D image rotation, a very relevant operation for realistic images, but is invariant with respect to row/column permutations, which are not a relevant operation for realistic images.
In general it doesn't make sense to compress images this way, since the algorithm is not invariant with respect to 2D image rotation, a very relevant operation for realistic images, but is invariant with respect to row/column permutations, which are not a relevant operation for realistic images.