Arriving soon at your local Boeing Surplus store

The ultimate room acoustic treatment...
I wonder if the compressed air in this "wallpaper" is varied in a controlled and constant way, acting as the engine to power the material itself. The entire outer surface would act as a giant radiator or loudspeaker.

For this to work, it would require a microphone to pick up unwanted noise and generate the inverse to drive the wall covering.

If the idea is based on constant pressure compressed air only, they must really be on to something. Without this being active I don't understand how such thin material would be effective against low frequency sound.
Can't say for sure what they're on to but Piper Aircraft and Beechcraft have inflatible door seals that dramatically reduce inflight noise. The effect is from both the air in the seal and by better filling the gaps between door and fusealge
Very exciting! My guess is the denser compressed air is reacting to the low frequency sound waves differently than the surrounding air. The "smart" material is holding the wave or oscillation in the compressed air. The overall area covered by the material is then used to absorb the wave. Rather than thinking of it as a thin layer, think of it in the other two dimensions, height and width. The area is immense, even the longest wave length could be handled. It's all in the ability of the "smart" material and the compressed air?