A pseudoinverse update algorithm for rank-reduced covariance matrices from 2-D data

A number of algorithms have a higher resolution than the common beamformer. These often require the calculation of a pseudoinverse of a matrix, which makes the algorithm very slow for repeated applications. We consider updating the pseudoinverse for window motions either in time or in space for two-dimensional (2-D) data taken from a linear array. Our results are shown to reduce the computational complexity of the multiple sidelobe canceller (MSC), for example, by more than 75% for a downward window movement (with time) and more than 55% for a sideways window movement (across traces).