When you inflate this basketball (something that is frequently done), an additional very high-pressure air container is also filled.
When the ball detects impact, part of this compressed air is released inside the ball, causing it to expand enough to bounce. Upon bounce, mini-vents open and let out
just enough air to bring the pressure inside the ball back to what it was before the ball hit the ground.
The result is a basketball that bounces higher and higher each time unless caught (or until the compressed air runs out).
It may prove to be easier (if a bit less uniform) to use pneumatic actuators inside the ball rather than simply letting more air in.