I am trying to make a backup (a direct dd image of the partitions of my built-in memory card of my phone to my PC. I am using Linux and my phone is a Nexus 4.
Here another better answer:
Requirements: adb must be already installed
From your Linux PC in the folder where boot.img is located type:
$ fastboot boot boot.img
To copy the image of the mmcblk0 partition type:
$ adb pull /dev/block/mmcblk0 mmcblk0.img