I've just found some info by searching on the web...
- Many users with url issue (and bad SEO) due to image name rewriting, and still some bugs in the mod_pagspeed (view some issues reported on the mod_pagespeed github).
- Does not work well with WordPress, Drupal, Joomla... And need to use only minimum settings (no filters).
blog.webfaction.com/2010/11/speed-up-you...-with-mod_pagespeed/
- Seems not easy to use properly on a joomla site..., but check if all joomla cache is disable when using mode_pagespeed :
github.com/pagespeed/mod_pagespeed/issues/129
- ...
I would recommand to better use a Joomla integrated solution such as JCH Optimize plugin
Another info (found in French) with someone having a lot of issue with Joomla and mod_pagespeed, and had to disable mod_pagespeed.
Then, to rewrite url to more friendly SEO url for all images, you can check its code for htaccess :
forum.joomla.fr/archive/index.php/t-213626.html
Another post, with another issue with mod_pagespeed :
groups.google.com/forum/#!msg/mod-pagesp...fHIxoQU/hy0lqb0NBwAJ
So... if you really want to use mod_pagespeed, a special setting should be found to work on Joomla (as i think that all your images are renamed in the media manager, no ?)
Best Regards,
Cyril