We consider the estimation of multiple room impulse responses from the simultaneous recording of several known sources. Existing techniques are restricted to the case where the number of sources is at most equal to the number of sensors. We relax this assumption in the case where the sources are known. To this aim, we propose statistical models of the filters associated with convex log-likelihoods, and we propose a convex optimization algorithm to solve the inverse problem with the resulting penalties. We provide a comparison between penalties via a set of experiments which shows that our method allows to speed up the recording process with a controlled quality tradeoff.