###### Abstract  
For adaptive ultrasound imaging, a reliable estimation of the covariance matrix has a decisive influence on the performance of beamformers. In this paper, we propose a new cross subaperture averaging generalized sidelobe canceler approach (GSC-CROSS) for medical ultrasound imaging, which uses the cross-covariance matrix instead of the traditional covariance matrix estimation. By using the more stable and accurate estimation of the covariance matrix, GSC-CROSS performs well in both lateral resolution and contrast. Experiments are conducted based on the simulated echo data of scattering points and a cyst target. Beamforming responses of scattering points show that GSC-CROSS can improve the lateral resolution by 76.9%, 68.8%, and 17.1% compared with delay-and-sum (DS), synthetic aperture (SA), and the traditional generalized sidelobe canceler (GSC), respectively. Also, imaging of the cyst target shows that compared with DS, SA, and GSC, the contrast increases by 101%, 32.6%, and 63.5%, respectively. Finally, the actual echo data collected from a medical ultrasonic imaging system is applied to reconstruct the image. Results show that the proposed method has a good performance on lateral resolution and contrast. Both the simulated and experimental data demonstrate the effectiveness of the proposed method.  
GSC-CROSS; adaptive beamforming; minimum variance; covariance matrix +
Footnote †: journal: Medical Ultrasound Imaging  
generalized sidelobe canceler beamforming for medical ultrasound imaging systems [15]. By separating the linear constraint space, GSC converts the constrained problem of the adaptive beamforming algorithm into an unconstrained problem, thus overcoming the signal cancellation problem of MV [16; 17].  
For adaptive beamforming, due to the high correlation of medical ultrasonic echo signals [18], some processing algorithms must be introduced to eliminate the correlation. The commonly used method is the subaperture averaging proposed by [PERSON] [19]. However, obtaining the covariance matrix with the subaperture averaging, the performance of GSC will approach the non-adaptive beamformer (SA) as the number of subarrays increase. Furthermore, although the lateral resolution improved, the contrast did not improve correspondingly. Therefore, how to obtain a reliable estimate of the covariance matrix that can simultaneously improve the lateral resolution and contrast has become a research hotspot.  
In this paper, we put forward a new cross subaperture averaging generalized sidelobe canceler algorithm (GSC-CROSS) for medical ultrasound imaging, which uses echo signals from different subarrays to calculate a cross-covariance matrix. By using the more stable and accurate cross-covariance matrix instead of the traditional subaperture averaging one, the quality of the echo image improves significantly. Simulated and experimental results show that this method can improve both lateral resolution and contrast of the image and the performance is stable under different numbers of subarrays.  
The outline of this paper is as follows: In Section 2, we introduce the mathematical model of ultrasound imaging and the basic principles and application methods of the GSC. In Section 3, we explain the basic principle and realization of GSC-CROSS in detail. Moreover, we show the experimental results based on simulated and actual echo data in Section 4. In Section 5, we discuss the advantages of the proposed method and compare it with other beamformers. Finally, conclusions of the study are provided in Section 6.