You will need to first find a full backup which has data in the table. Once you have found that backup, restore it again with NORECOVERY. Then you can apply transaction logs to that backup. If think you could use the STANDBY option for the logs you apply, so you that you can peek into the the database as readonly. Keep on doing this until you find the table empty. Then you will have to start over to restore the log before the table was cleared.
Keep in mind that BACKUP and RESTORE do not work with tables. They work with pages, and do not really know what are on these tables.
(I'm a little bit out of my league here. I trust Sashank or Tibor to correct me if I say something completely wrong.)