Recover Picasa people/face data
From Picasa Resources

By default, Picasa stores the face tags in the (hidden) .picasa.ini files in the folder where the picture is located on your hard disk.
But... it is a lot safer that you let Picasa store the face tag information inside .jpg files:
start Picasa, go to &quot;Tools&quot;/&quot;Options&quot; in the menu. On the Name Tags tab, put a check mark by the Store name tags in photo option. When you have this option checked, any new faces that you tag will be stored inside the photo in the standard XMP Metadata section. This does not affect existing face tags.
Setting the previous option only takes care that all future name tags are added into the XMP metadata section. To have all existing face tags saved in the .jpg, go to &quot;Tools&quot;/&quot;Experimental...&quot;/&quot;Write faces to XMP...&quot; and choose &quot;Write faces&quot;.  The Write Faces process will take some time, because it has to write all the face tags to all the photos in your photo collection, so take a break and let it do it's work.

In light of this - I would recommend finding the hidden files on your previous backup, and replacing them on your machine, or adding them if they don't exist. From there, you can follow the instructions above to write the data into the images themselves.