If you know the offsets and sizes of the partitions that you used to have, then you can just recreate them in your new partition table. The filesystems are still where you left them, so once the partition table is reconstructed, everything should start working again.

If you don't know that info, I am not sure what you do. Some kind of recovery utility could probably find your data without too much issue, but I am not too familiar with the current state of disk recovery tools.