About restores of a database that contain full-text catalog
As of SQL Server 2008 and later, full-text search catalogs are included in the database backup and are restored as a part of the recovery process. When you restore a filegroup, NetBackup restores the full-text index files and other files in the filegroup. For additional information on backing up and restoring full-text catalogs and indexes, see the following Microsoft article.
https://msdn.microsoft.com/en-us/library/ms142511.aspx
If you want to back up and restore the full-text catalogs that you upgraded from SQL Server 2005, refer to the following Microsoft article: