image paths have double slashes '//; how to fix this

The Issue:
Here is an example image path:
…./home/tbed//wp-content/uploads/2013/07/julyaug2013_forslider_sanstext6.png
Note how after “tbed” there is a double //.
I see this path in a “edit media” page that I invoke from Media Library/edit. I am guessing that it is this // that prevents me from seeing thumbnails, and if I click “view” from Media Library, I cannot see the image, just the image title. Also, even though images on various posted Pages display correctly, I can see still the // in the html.

I have moved this website several times (see below for the mechanism) and the // is true for all the legacy images in the website. But if I upload new images to Media Library, all is well — from that I conclude that the internal workings of my WordPress installation are ok.

What I would like is to do some sort of automated update (on the WP database??) to fix this. I would rather NOT have to upload again all the legacy images as the fix.

However, when I look in my wp_postmeta table at the meta_value column, there is no / at the beginning of the entry; rather the format of good and bad image entries look the same. (So maybe the problem is not in the database. ??) Yet since new entries work fine, then the problem is not in a setting somewhere within the WP admin interface, right?

Also, when I run the plugin: Regenerate Thumbnails, I see errors like this:

julyaug2013_forslider_sanstext7 (ID 392031) failed to resize. The error message was: The originally uploaded image file cannot be found at

The line terminates after the “at”.

I am not skilled enough in the php language to trace the code within the WP files to see how WP is composing the image paths.

Any suggestions how to fix these paths??

—Mechanism for moving WordPress websites.
I have used several times the php code found at doezema to help me move my website from one server to another. So far it has worked without error, so I am hoping that is not the problem.