Colorization Using Optimization (2004)
cs.huji.ac.il
cs.huji.ac.il
Of course lossy compression uses other tricks like using different color representations (YUV, YCbCr) where the techniques described in this article may not work, and downsampling, but at least it could be an improvement over lossless image compression?
However, the general idea of getting better color from luma channel has been tried in Daala: https://people.xiph.org/~xiphmont/demo/daala/demo4.shtml and a form of that has been added to the AV1 codec.
[1] Zhang, Richard, Phillip Isola, and Alexei A. Efros. "Colorful image colorization." European Conference on Computer Vision (2016) http://richzhang.github.io/colorization/