Computationally Efficient Adaptive Beamformer for Ultrasound Imaging Based on QR Decomposition

Adaptive beamforming methods for ultrasound imaging have been studied to improve image resolution and contrast. The most common approach is the minimum variance (MV) beamformer which minimizes the power of the beamformed output while maintaining the response from the direction of interest constant. The method achieves higher resolution and better contrast than the delay-and-sum (DAS) beamformer, but it suffers from high computational cost. This cost is mainly due to the computation of the spatial covariance matrix and its inverse, which requires O(L
³
) computations, where L denotes the subarray size. In this study, we propose a computationally efficient MV beamformer based on QR decomposition. The idea behind our approach is to transform the spatial covariance matrix to be a scalar matrix σI and we subsequently obtain the apodization weights and the beamformed output without computing the matrix inverse. To do that, QR decomposition algorithm is used and also can be executed at low cost, and therefore, the computational complexity is reduced to O(L
²
). In addition, our approach is mathematically equivalent to the conventional MV beamformer, thereby showing the equivalent performances. The simulation and experimental results support the validity of our approach.