Updating column value to the ID associated with it in another table.

Ok working on someone else's code I've run into the following problem with their photo gallery. There is a table to store the image, image path, gallery, etc... and a table to store the gallery name, a short name (for the url) and an id for the gallery. However the image table is story the short name for the gallery instead of the id. Example data:

gallery_images:

+------------------------------------------------------------------------------+
|id_image|img_filename|img_ext|img_path|  img_gal  | img_date |img_photographer|
+--------+------------+-------+--------+-----------+----------+----------------+
|   1    | dsc_004    | jpg   | ...    | golf_2011 |2011-06-10| My Name        |
|   2    | dsc_027    | jpg   | ...    | golf_2011 |2011-06-10| My Name        |
|   3    | dsc_523    | jpg   | ...    | dtco_2011 |2011-09-20| Someone's Name |
|   4    | dsc_544    | jpg   | ...    | dtco_2011 |2011-09-20| My Name        |
.....

Select allOpen in new window

gallery_groups

+--------------------------------------+
|id_gal|  gal_name         | gal_short |
+------+-------------------+-----------+
|   1  | 2011 Golf Outting | golf_2011 |
|   2  | 2011 Celebrity ...| dtco_2011 |
...

Select allOpen in new window

What I'm trying to do is create a query, that will update the gallery_images table, img_gal column to instead have the id of the gallery as listen in the gallery_groups table.