I do have a very water-damaged tile floor on the patio. Is there any way/procedure that can save these tiles? Or do I have to tear it all out and replace these tiles?

http://www.flickr.com/photos/forschende/5040533121/

The latter, of course, I would like to avoid.

Thank you for helping :-)

Greetings, handynovice

PS. Of course, I were not that careless; I took over this mess with the house :-(