These are messages not photos or videos. The text messages are stored internally on the phone itself. If the messages are deleted there is no recovering them.
The only way to get them back is to do as inzone says above.
Carriers keep logs of every message sent and received in their servers for legal purposes. Say the police believe someone has been trafficking drugs using the phone to take orders. They would get a warrant and the phone company would give them a copy of all the messages to look over for incriminating evidence.
Some carriers have options available online where you can see the messages and send them to yourself. Others you will have to request it.