High Resolution Minimum Variance Beamformer With Low Complexity in Medical Ultrasound Imaging.

Although the minimum variance beamformer (MVB) shows a significant improvement in resolution and contrast in medical ultrasound imaging, its high computational complexity is a major problem in a real-time imaging system. Therefore, it seems necessary to propose a new method with a lower computational complexity that preserves the advantages of the MVB. In this paper, the MVB was implemented with a partial generalized sidelobe canceler (GSC) with a blocking matrix based on our previous study, which projected the incoming signals to a lower dimensional space. The partial GSC separated the weight vector into one fixed and one adaptive weight, whereby the optimization could be performed with lower complexity on the adaptive part. In addition, this dimension reduction allowed us to increase the length of the subarray when using a spatial smoothing method, which was used to decorrelate the incoming signals. The subarray length was limited to half the length of the full array size in the ordinary MVB, while the proposed beamformer could cross over this limitation. The results demonstrated that the point spread function of the proposed beamformer was about 6.3 times narrower than the classic MVB, while the contrast was almost saved. These results were achieved with linear computational complexity by the proposed method, while it was cubic for the MVB. For a sample scenario, the proposed method needed only 1.8% of the required ops of the MVB.

Iterative Minimum Variance Beamformer with Low Complexity for Medical Ultrasound Imaging.

Minimum variance beamformer (MVB) improves the resolution and contrast of medical ultrasound images compared with delay and sum (DAS) beamformer. The weight vector of this beamformer should be calculated for each imaging point independently, with a cost of increasing computational complexity. The large number of necessary calculations limits this beamformer to application in real-time systems. A beamformer is proposed based on the MVB with lower computational complexity while preserving its advantages. This beamformer avoids matrix inversion, which is the most complex part of the MVB, by solving the optimization problem iteratively. The received signals from two imaging points close together do not vary much in medical ultrasound imaging. Therefore, using the previously optimized weight vector for one point as initial weight vector for the new neighboring point can improve the convergence speed and decrease the computational complexity. The proposed method was applied on several data sets, and it has been shown that the method can regenerate the results obtained by the MVB while the order of complexity is decreased from O(L3) to O(L2).

A low complexity minimum variance beamformer for ultrasound imaging using dominant mode rejection.

In recent years, high resolution adaptive minimum variance-based beamformers have been successfully applied to medical ultrasound imaging to improve its resolution and contrast, simultaneously. However, these improvements come at the cost of much more computational complexity in comparison to the non-adaptive delay-and-sum beamformer. The computational overhead mainly results from the L×L covariance matrix inversion needed for computation of the adaptive weights, the complexity of which is cubic with the subarray size, O(L3). In medical ultrasound imaging with focusing on the imaging point, we have a limited number of dominant modes and there is no need for the full matrix inversion. Based on this idea, we have investigated the application of the dominant mode rejection (DMR) adaptive beamformer for medical ultrasound imaging, which uses only some largest dominant modes to approximate the covariance matrix in dominant subspace. We show, using simulated and experimental data, that this subspace dimension can be selected as low as two resulting in significant computational complexity reduction while still achieving performance comparable to that of the minimum variance beamformer.

Low complex subspace minimum variance beamformer for medical ultrasound imaging.

Minimum variance (MV) beamformer enhances the resolution and contrast in the medical ultrasound imaging at the expense of higher computational complexity with respect to the non-adaptive delay-and-sum beamformer. The major complexity arises from the estimation of the L×L array covariance matrix using spatial averaging, which is required to more accurate estimation of the covariance matrix of correlated signals, and inversion of it, which is required for calculating the MV weight vector which are as high as O(L(2)) and O(L(3)), respectively. Reducing the number of array elements decreases the computational complexity but degrades the imaging resolution. In this paper, we propose a subspace MV beamformer which preserves the advantages of the MV beamformer with lower complexity. The subspace MV neglects some rows of the array covariance matrix instead of reducing the array size. If we keep η rows of the array covariance matrix which leads to a thin non-square matrix, the weight vector of the subspace beamformer can be achieved in the same way as the MV obtains its weight vector with lower complexity as high as O(η(2)L). More calculations would be saved because an η×L covariance matrix must be estimated instead of a L×L. We simulated a wire targets phantom and a cyst phantom to evaluate the performance of the proposed beamformer. The results indicate that we can keep about 16 from 43 rows of the array covariance matrix which reduces the order of complexity to 14% while the image resolution is still comparable to that of the standard MV beamformer. We also applied the proposed method to an experimental RF data and showed that the subspace MV beamformer performs like the standard MV with lower computational complexity.

Amplitude and phase estimator combined with the Wiener postfilter for medical ultrasound imaging.

BACKGROUND: The adaptive amplitude and phase estimator (APES) has been introduced in medical ultrasound imaging to calculate the amplitude of the desired signal more robustly than other adaptive beamformers like minimum variance (MV). This beamformer minimizes the optimization problem of MV by replacing the estimated array covariance matrix by the interferences plus noise covariance matrix. On the other hand, the Wiener postfilter as a post-weighting factor, which will be multiplied to the final weight vector of the beamformer, estimates the power of the desired signal and the power of the interferences plus noise to improve the contrast. METHOD: The proposed method is a combination of the APES beamformer with the Wiener postfilter which uses the capabilities of the APES beamformer for accurate estimation of the amplitude of the desired signal and the Wiener postfilter in suppressing sidelobes. Specifically, we used the interferences plus the noise covariance matrix estimated in the APES beamformer to obtain an APES-based Wiener postfilter and obtained the APES + Wiener weight vector by multiplying the APES-based Wiener postfilter to the standard APES weight vector. RESULTS: To evaluate the proposed APES + Wiener beamformer, we tested the proposed method on simulated and experimental datasets. The results of a simulated wire phantom demonstrate that the proposed beamformer can resolve two point scatterers better than the standard APES beamformer, even if the points are placed near each other. Simulating a cyst phantom shows that the APES + Wiener beamformer improves the contrast of the resulting images by about 4.5 dB by estimating the interior of the cyst better than the standard APES. CONCLUSION: The evaluation of the proposed beamformer on an experimental dataset confirms the results of simulations, in which the proposed beamformer improves the resolution and contrast in comparison with the standard APES beamformer.