I have a 1TB HDD and some days ago I did a mess

That disk had:

• One EXT3 partition ( / )


• One EXT3 partition ( /boot )


• One LUKS LVM which had a EXT3 partition of about 200 GB

I wanted to replace Linux Mint 14 with Ubuntu 14.04, so I booted Ubuntu 14.04 from USB and did the installation wizard.
The wizard asked me "Replace Linux Mint 14 with Ubuntu 14.04", so I did, I also checked to add LVM and to crypt user directory. I set up a password and I installed it.

The installation blocked itself almost at end, and by rebooting via USB i noticed that the HDD was formatted and there was just the /boot and the / (my LUKS LVM was formatted and replaced with those two partitions)

I have

• The disk itself


• The dd image of the disk after the disaster (a 1TB img)


• The passphrase to unlock both the LVM: the oldest one (which I want to recover) and the newest one (to unlock the root partition)

Question

How can I recover my precious data?