Empirical Bayesian regularization of the inverse acoustic problem

This paper answers the challenge as how to automatically select a good regularization parameter when solving inverse problems in acoustics. A Bayesian solution is proposed that consists either in directly finding the most probable value of the regularization parameter or, indirectly, in estimating it as the ratio of the most probable values of the noise and source expected energies. It enjoys several nice properties such as ease of implementation and low computational complexity (the proposed algorithm boils down to searching for the global minimum of a 1D cost function). Among other advantages of the Bayesian approach, it makes possible to appraise the sensitivity of the reconstructed acoustical quantities of interest with respect to regularization, a performance that would be otherwise arduous to achieve.