The Recovery Machine in My Time at Portia allows you to restore Relics, which you must do if you want to donate it to the Museum. You begin the game by using the Recovery Machine at the Research Center, but you are also able to get one for yourself later in the game.
In order to get your own Recovery Machine, you will need to have donated at least 10 different Relics, Fish, or Artwork to the Museum. Once you reach a total of 10 items donated, you will get the Recovery Machine as a reward. At this point you can place it in your home to make it much easier to restore the Relics you find.
There are currently no other ways to obtain your own Recovery Machine, so you better get Relic hunting if you want to have this station for yourself.