Thing I'd love to try if I had time - a compressor which derives the best table for the image. I'm imagining a loop of: start with the default, compress, calculate the difference from the original, dct the error to see which patterns are missed, adjust the table, repeat. Stop on some given error/size-increase ratio. (yes, I'm trying to get someone else nerd sniped into doing this)
Edit: something like this https://www.imaging.org/site/PDFS/Papers/2003/PICS-0-287/849...
So from the older known ones there DCTune and DCTex methods, but it seems neither is available for download anywhere.
MozJPEG [1] includes several quantization tables that are optimized for different contexts (see the quant-table flag and source code for specific tables[2]), and the default quantization table has been optimized to outperform the recommended quantization tables in the original JPEG spec (Annex K).
It's also worth noting that MozJPEG uses Trellis quantization [3] to help improve quality without a per-image quantization table search. Basically rather than determining an optimal quantization table for the image, it minimizes rate distortion on a per-block level by tuning the quantized coefficients.
Both the SSIM and PSNR tuned quantization tables (2 and 4) provided by MozJPEG use a lower value in the first position of the quantization just like this article suggests (9 and 12 vs the libjpeg default of 16).
[1] https://github.com/mozilla/mozjpeg
[2] https://github.com/mozilla/mozjpeg/blob/5c6a0f0971edf1ed3cf3...