The singular value decomposition is doing the same thing as the DCT, sort of. It’s transforming the image into coefficients where the important coefficients are packed in one location. It’s worth applying similar techniques. You can see the demo where it’s truncating the coefficients.

Half the image codecs out there look like JPEG if you squint hard enough. That’s ok, “reimplementing a thing approximating” another codec is how a lot of marginal improvements have been made in the past, and if you add up enough marginal improvements, you end up with a competitive new codec in its own right.

The DCT isn’t magic, it just happens to work really well and requires little computational power. There’s a lot of possibilities for replacing the DCT with something else, especially now that we have more computational power to throw around.