Kudos to my Gast 1/4hp pump that has been in use for over a year averaging about 8 hours a day. I would say the the pump by itself, on the workbench running, is about as noisy as a loud vacuum cleaner. It gets louder the more back pressure it realizes, but not much louder.
I think you could really get the sound levels down using an aircrete box with aircrete lid or soundproofed roof (I'd use foam and wood for the roof with plastic or sheet metal cap if an aircrete roof is not doable). The key will be venting the air passages so that they direct the noise away from any areas that people will be.
I have no experience with the Matala.
You should do a DIY aircrete pump house thread!