Image Compression using SVD

Question

I've been researching on image compression with SVD for school. However, I do not see how there will be a reduction in memory by using SVD and truncating the number of singular values used. The original image would be m x n in size, thereby using m x n x pixel-size bytes. After SVD the resultant matrix is still m x n. Would it not then use the same amount of space?

Answer 1

That's because the rank-k approximation of the image requires you to store (think about saving the image into a file) only the first k singular vectors and singular values, resulting in a m x k storage space instead of m x n. Then, when you want to render the image on screen you are obviously uncompressing it back to the m x n size (as you do with any other kind of compression), but that's not the true size of the image, is only rendering.