Acoustic imaging using under-determined inverse approaches: Frequency limitations and optimal regularization

This paper presents an acoustic imaging technique based on an under-determined inverse approach. The principle is to quantify an elementary source distribution on a source surface from acoustic pressure measurements. The acoustic transfer system between elementary sources and microphone positions, very under-determined, is then reduced to a square system using singular value decomposition. The high frequency limitation of this method is studied, as well as the regularization techniques that have to be used at low frequency. A Monte-Carlo simulation is carried out to compare the efficiency of generalized cross validation and L-curve validation to choose the Tikhonov regularization parameter. A combined validation criterion is finally proposed to take advantage of both approaches.