Low complex subspace minimum variance beamformer for medical ultrasound imaging

Minimum variance (MV) beamformer enhances the resolution and contrast in the medical ultrasound imaging at the expense of higher computational complexity with respect to the non-adaptive delay-and-sum beamformer. The major complexity arises from the estimation of the L×L array covariance matrix using spatial averaging, which is required to more accurate estimation of the covariance matrix of correlated signals, and inversion of it, which is required for calculating the MV weight vector which are as high as O(L(2)) and O(L(3)), respectively. Reducing the number of array elements decreases the computational complexity but degrades the imaging resolution. In this paper, we propose a subspace MV beamformer which preserves the advantages of the MV beamformer with lower complexity. The subspace MV neglects some rows of the array covariance matrix instead of reducing the array size. If we keep η rows of the array covariance matrix which leads to a thin non-square matrix, the weight vector of the subspace beamformer can be achieved in the same way as the MV obtains its weight vector with lower complexity as high as O(η(2)L). More calculations would be saved because an η×L covariance matrix must be estimated instead of a L×L. We simulated a wire targets phantom and a cyst phantom to evaluate the performance of the proposed beamformer. The results indicate that we can keep about 16 from 43 rows of the array covariance matrix which reduces the order of complexity to 14% while the image resolution is still comparable to that of the standard MV beamformer. We also applied the proposed method to an experimental RF data and showed that the subspace MV beamformer performs like the standard MV with lower computational complexity.