Someone has converted a number of JPG's to BMP's, and then to PNG, under the assumption that it will "increase quality". Of course, it doesn't, as once you've introduced lossy compression you can never get anything "better" than that.
So now the problem is, BMP's are big. I can use lossless formats like 24bpp PNG, but they are still bigger than the "original" JPG's, despite being identical images.
Is it possible to return those BMP's back to JPG's without introducing additional artifacts? My impression is no, but maybe I'm wrong?