Optimal beamforming using higher order statistics for passive acoustic mapping

Passive Acoustic Mapping (PAM) of sources of nonlinear acoustic emissions has been extensively investigated for monitoring ultrasound therapies. Optimal data-adaptive beamforming algorithms, such as Robust Capon Beamformer (RCB), were readily proposed as a means of improving source localization, accounting simultaneously for array configuration and calibration errors. RCB, however, assumes that signal samples follow a Gaussian distribution. Aiming at improving the spatial resolution of PAM, especially in the axial direction with respect to the array, we propose an alternative beamforming approach, Robust Beamforming by Linear Programming (RLPB). This method makes no assumptions on the statistical distribution of the received signals, and exploits not only the variance but also higher-order-statistics (HOS) of the received signals. Performance evaluation on simulated and in vitro experimental data suggests improvement in spatial resolution on the order of 20% and 15% in the axial and transverse directions respectively. This facilitates real-time mapping of disjoint cavitating regions over biologically relevant lengthscales on the order of 2 mm in the axial direction. It is expected that the proposed beamforming approach will provide the necessary improvement in PAM spatial resolution required in several clinically relevant situations, where a single array is used and the ratio of depth to aperture becomes large.