Legendre polynomial based fast minimum variance beamforming method for medical ultrasound systems

Recently, minimum variance beamforming (MV BF) has been actively investigated as a method to improve the performance of an ultrasound system beamformer, especially in terms of both the lateral and contrast resolution. However, since the inverse spatial covariance matrix must be calculated, a severe problem with the method is the prohibitive computational complexity. Among numerous attempts to overcome the problem, notable ones are the fast MV BF method based on principal component analysis and beam space adaptive beamforming. The two are similar in transforming an original signal in the element space to the other domain using an orthonormal basis matrix and approximating the covariance matrix with dimensionality reduction in the transformed domain, hence simplifying the inversion of the matrix. A new method that uses the Legendre polynomial as the basis matrix for such transformation is proposed. The efficacy of the proposed method is verified through Field II simulation. Computer simulation results show that the proposed method is better than or almost equal to the above two methods in the approximation error and the lateral response.