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Recently, adaptive beamforming methods have been successfully applied to medical ultrasound imaging, resulting in significant improvement in image quality compared with non-adaptive delay-and-sum (DAS) beamformers. Most of the adaptive beamformers presented in the ultrasound imaging literature are based on the minimum variance (MV) beamformer which can significantly improve the imaging resolution, although their success in enhancing the contrast has not yet been satisfactory. It is desirable for the beamformer to improve the resolution and contrast at the same time. To this end, in this paper, we have applied the eigenspace-based MV (EIBMV) beamformer to medical ultrasound imaging and have shown a simultaneous improvement in imaging resolution and contrast. EIBMV beamformer utilizes the eigenstructure of the covariance matrix to enhance the performance of the MV beamformer. The weight vector of the EIBMV is found by projecting the MV weight vector onto a vector subspace constructed from the eigenstructure of the covariance matrix. Using EIBMV weights instead of the MV ones leads to reduced sidelobes and improved contrast, without compromising the high resolution of the MV beamformer. In addition, the proposed EIBMV beamformer presents a satisfactory robustness against data misalignment resulting from steering vector errors, outperforming the regularized MV beamformer.