Filesystem restored from e2image appears corrupt after replaying journal

Issue

e2fsck reports serious errors after replaying journal on a e2image:

e2fsck 1.41.14 (22-Dec-2010)
/dev/loop0: recovering journal
e2fsck: Group descriptors look bad... trying backup blocks...
e2fsck: Bad magic number in super-block when using the backup blocks
e2fsck: going back to original superblock
Note: if several inode or block bitmap blocks or part
of the inode table require relocation, you may wish to try
running e2fsck with the '-b 32768' option first.  The problem
may lie only with the primary block group descriptors, and
the backup block group descriptors may be OK.
...