iPad Mini - Stuck in black Apple & White Background loop
Absolutely. This is a problem that has been bothering people for a while but luckily there is a very common solution as the issue is only temporary.

Option 1  


Hold down the Home and Power button until the phone reboots.
Let go of the Power button but keep holding down the Home button until you get back to the lock screen.


Option 2  


Hold down the Home and Power button until the phone reboots.
On reboot, hold the volume up button until you are back at the lock screen.


Both of these options force a reboot, which in the majority of cases, is all you need to do.
Let me know if that makes sense to you and report back with the option that worked for you. I'd be interested to follow up with you on this.