Applying constraint to minimum variance problem to provide a computationally efficient beamformer for medical...

Minimum variance (MV) beamforming was introduced in ultrasound imaging to improve image quality. It solves a minimization problem where the closed-form solution imposes huge computational load due to the matrix inversion requirement. The MV problem can be iteratively solved to avoid this requirement.

This paper shows that the weight vector at the first iteration is proportional to the covariance matrix elements. It is proposed that this proportionality be considered as a constraint in the main MV problem. Inspired by the idea of the exact line search method, solving the proposed constrained MV (CMV) problem leads to an adaptive beamforming with considerably lower computational load. As an interesting point, the unknown coefficients can be directly calculated through entries of a covariance matrix by a simple operation.

The proposed method was investigated on several simulation and experimental data sets. It was found that it required 93% fewer flops than the MV method, which represents a dramatic computational gain.

This study showed how only two features, the mean and trace of the covariance matrix, are enough to achieve adaptive beamforming. The proposed beamformer provides approximately the same resolution as the MV method.