This looks like a diaphragm pump? These are mostly pretty noisy from the ones I have seen, but you could try minimising the amount of vibration by putting a pad of thick rubber or neoprene between the feet and your wall? Also some will be transferring down the pipes, this is a bit harder to isolate, but you would be surprised how effective a few strategically placed pieces of foam can be.
I do this for larger air pumps and it makes a big difference. I have noticed more recently there are some companies that have been producing some very high pressure low db pumps for misting systems.
Is one who’s pumps I have looked at for high pressure aeroponics, the are surprisingly quiet and capable of up to 120 psi, so if you need the 50psi of pressure or more the pump you have is putting out when it gives up the ghost you could look at something like these?