As far as I know, the Linux LVM kernel driver can only use block devices as physical volumes, and I'm not aware of any userland tools to access LVM volumes conveniently. So you need to make the physical volume appear as a loop device. (I assume you're running Linux; if not, run it, in a virtual machine if necessary.)
First, determine the offset of the partition. You can use
fdisk for that:
fdisk -lu /path/to/disk.image
Note the offset of the partition you want (in the
Start column), e.g. 123456. The unit is 512-byte sectors. Now create a loop device from the image, starting at the desired offset.
losetup -fv -o $((123456*512)) /path/to/disk.image
The partition will be available as the block device
/dev/loop0 (the number may be different if you already have active loop devices).
There's a patch to the Linux kernel to access partitions on a loop device automatically. Debian applies it in its stock kernel; most other distributions don't. If you have this patch, you can run
losetup -fv /path/to/disk.image and access the partitions on the device as e.g.
/dev/loop0p1 and so on. You may need to pass an explicit argument to the driver to enable this feature:
rmmod -r loop && modprobe loop max_part=63.
pvscan. This should pick up
/dev/loop0p1 or whatever the device name turns out to be as a physical volume. You can then activate the volume group(s) on it with
vgchange -ay and the access the logical volumes under