Inversion of modified beamformed array data

TL;DR: This work describes three methods of inverting the beamformer output to reconstruct the space-time samples, and describes a block matrix inversion technique, which is new and exact when operating on the original data, but fails when thebeamformer output is modified.

Abstract: The separation of transient plane-waves as a function of their velocity and time-of-arrival can be performed by a time domain beamformer. Modifications in the beamformer output domain, such as masking out coherent interfering signals while taking into account both velocity and time information, are more straightforward than with traditional (k-ω) velocity filtering methods. We describe three methods of inverting the beamformer output to reconstruct the space-time samples. Of the three, one method, a block matrix inversion technique, is new. It is exact when operating on the original data, but fails when the beamformer output is modified. This problem can be alleviated by reducing the dimensionality of the inversion matrix using a singular value decomposition.