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In recent years, adaptive beamforming methods have been successfully applied to medical ultrasound imaging, resulting in simultaneous improvement in imaging resolution and contrast. These improvements have been achieved at the expense of higher computational complexity, with respect to the conventional non-adaptive delay-and-sum (DAS) beamformer, in which computational complexity is proportional to the number of elements, O(M). The computational overhead results from the covariance matrix inversion needed for computation of the adaptive weights, the complexity of which is cubic with the subarray size, O(L3). This is a computationally intensive procedure, which makes the implementation of adaptive beamformers less attractive in spite of their advantages. Considering that, in medical ultrasound applications, most of the energy is scattered from angles close to the steering angle, assuming spatial stationarity is a good approximation, allowing us to assume the Toeplitz structure for the estimated covariance matrix. Based on this idea, in this paper, we have applied the Toeplitz structure to the spatially smoothed covariance matrix by averaging the entries along all subdiagonals. Because the inverse of the resulting Toeplitz covariance matrix can be computed in O(L2) operations, this technique results in a greatly reduced computational complexity. By using simulated and experimental RF data-point targets as well as cyst phantoms-we show that the proposed low-complexity adaptive beamformer significantly outperforms the DAS and its performance is comparable to that of the minimum variance beamformer, with reduced computational complexity.