/boot partition is nearly full; or a warning is received every time the system is rebooted.

Confirm this is the case:

df
ls /boot/

sudo apt-get purge linux-image-x.x.x-x

The headers are installed into /usr/src and are used when building out-tree kernel modules.

ls /usr/src

Returns

linux-headers-4.4.0-21          linux-headers-4.4.0-34-generic  linux-headers-4.4.0-42          linux-headers-4.4.0-45-generic
linux-headers-4.4.0-21-generic  linux-headers-4.4.0-36          linux-headers-4.4.0-42-generic  linux-headers-4.4.0-47
linux-headers-4.4.0-31          linux-headers-4.4.0-36-generic  linux-headers-4.4.0-43          linux-headers-4.4.0-47-generic
linux-headers-4.4.0-31-generic  linux-headers-4.4.0-38          linux-headers-4.4.0-43-generic
linux-headers-4.4.0-34          linux-headers-4.4.0-38-generic  linux-headers-4.4.0-45

Delete unused source headers

rm -Rf /usr/src/linux-headers-4.4.0-21*