Assuming you are running Apache, you can try explicitly setting up cache lifetimes for certain files types and/or locations in the filesystem.
<FilesMatch ".(jpg|jpeg|png|gif)$">
Header set Cache-Control "max-age=604800, public" # 7 days
</FilesMatch>
or something like
ExpiresByType image/jpeg "access plus 7 days"
ExpiresByType image/gif "access plus 7 days"
ExpiresByType image/png "access plus 7 days"
Typically, I will group types of files by use in a single directory and set lifetimes accordingly.
Browsers should not request files at all until this ages have expired, but may not always honor it. You may want/need to futz with Last-Modified and ETag headers. There is lots of good info on the web about this.