Breathable painting for acoustic panels? I wanted to have a picture painted by my friend onto an acoustic panel in my room. I contacted some local companies working on such projects, but they work only with printing on this material. 

Fortunately one of the manufacturers responded to my e-mail and explained the issues I will meet. He explained to me that material behind the picture needs to "breathe", so the canvas can't be covered with thick layer of oil paint, and even shouldn't be primed. Do you have any solution to allow such picture "breathing"?

The "breathing" is necessary, because the canvas needs to have pores allowing the sound wave to pass through and be absorbed by the material behind the canvas.

I thought about painting without priming, but I am not a painter and I don't know why priming is so important. My painter says it is impossible to paint without priming, but he isn't a professional painter, rather enthusiast, and he doesn't think he knows all tricks allowing such things, but he is willing to get to know them.
I think your best choice would be to have the image painted first (on primed canvas, or whatever it takes), scan it/take a high quiality photograph of it, and have it printed onto the panel. 

Notes:


I have personally never worked with acoustic panels.
Yes, there are breathable materials you can paint/draw with (like ink, watercolours).
I couldn't find what material is used for acoustic panels.
There is a possibility of the painting materials affecting the quality of the sound absorption of the panel regardless of them being breathable. 
Apparently professionals print onto the panels, so it is know that this won't affect the quality of the panel.
Having the image painted first by all the necessary means will also, most likely, give you a better result imagewise.