Performing image equalisation and then Jpeg compression
I did some experiments. Equalizing, then compressing, resulted in a nearly 50% larger file.  Normalizing increased the filesize but not so much.  Normalizing, then equalizing, also increased the filesize by nearly 50%. All are JPEG quality 50, created with ImageMagick:

 - left: original (4540 bytes); right normalized (5467 bytes):





- left: equalized (7444 bytes); right: normalized, then equalized (7251 bytes)