Performing image equalisation and then Jpeg compression I'm trying to estimate what would be the result of first performing an histogram equalisation on an image, and then compressing it using JPEG.

I know that histogram equalisation increases the contrast in the image.
I also know the jpeg reduces the size of the image by removing the high frequencies from the frequency domain. Thus, it seems reasonable to me that performing histogram equalisation first would result in loosing more information, as it would increase the higher frequencies in the photo only for them to be later removed by jpeg.

Am I correct? If no, what am I missing?
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)