https://github.com/ilyakurdyukov/jpeg-quantsmooth (good for most mid-quality and high-quality images)
https://github.com/victorvde/jpeg2png (use for very low-quality images, slower)
jpeg-quantsmooth gives a sharper output (use "-q6" option).
jpeg2png output is a little blurry, but it does a better job of unblocking very low-quality images.
Another algorithm that should work but I haven't seen tried is edge-aware chroma upsampling. libjpeg uses nearest neighbor upscaling for the subsampled color planes, which is why JPEG looks so bad when there's a transition from eg saturated red to black.
I'm suggesting something like eedi3 (http://avisynth.nl/index.php/Eedi3) but guided by the luma plane.
Oh, you can also jointly optimize the YUV-RGB conversion because if the pixel ends up out of range in RGB space it is probably a compression artifact. I read a paper on this once but haven't seen it implemented.
Well, I meant better upsampling than bilinear interpolation, which blurs chroma.
"Oh, you can also jointly optimize the YUV-RGB conversion because if the pixel ends up out of range in RGB space it is probably a compression artifact."
Probably not, I suspect that the mozjpeg encoder may use this, so images with black on white text look better (artifact noise go beyond of range).