Flexible Minimum Variance weights estimation using principal component analysis

Minimum Variance (MV) beamforming has been studied for high resolution ultrasonic imaging. However, it is not easy for the MV beamformer to be implemented into a real time diagnostic system, because it requires too much computation time in calculating covariance matrix inversion. This paper introduces a flexible MV weight estimation that can dynamically reduce the matrix dimension using principal component transform. Principal components are estimated offline from pre-calculated conventional MV weights. It is assumed that all MV weights can be approximated by a linear combination of selected principal vectors. In this paper, flexible MV weight estimation is introduced by deriving a linearly approximated minimum variance criterion with a constraint using Lagrange multiplier. Our method does not directly calculate the MV weights but estimates the weights in the linear combination of the selected principal components. The combinational weights are a function of the inversion of a transformed covariance matrix whose dimension is identical to the number of the selected component vectors. Delay-and-sum (DAS), conventional MV, and flexible MV method were experimented on Field II simulation using point targets and cysts. Our method can reduce the dimension of the covariance matrix down to 2 × 2 while maintaining the good image quality of the minimum variance.