The author talks about JPEG, and says the principle is surprisingly similar, but the connection between the two is actually pretty direct. I will link a previous comment of mine from another discussion of SVD image compression to explain: https://news.ycombinator.com/item?id=34732922

To go from JPEG to lossy WebP (really, VP8 intra frames), the main differences are

(a) using smaller (4x4) transform blocks instead of 8x8,

(b) noticing that if you take just the first coefficient in each block, it looks like a lower resolution of the original image, and applying another 4x4 transform to those coefficients,

(c) adding more sophisticated prediction between blocks (e.g., subtract the pixel on the right edge of the previous block from all the pixels in the same row of the current block before transforming them, or something similar to predict in other directions),

(d) filtering along block edges to reduce blocking artifacts (many JPEG decoders do this, but WebP/VP8 make it a mandatory part of the standard), and

(e) using arithmetic coding instead of Huffman coding.

There are of course other minor differences in the details.

But the main mechanism that underlies both is a transform that can be derived from the SVD if one assumes a simple statistical model of natural image data.