On the Relationship Between Robust Minimum Variance Beamformers With Probabilistic and Worst-Case Distortionless Response Constraints

Although the minimum variance (MV) beamformer can provide enhancement in both resolution and contrast of ultrasound images when compared with conventional delay-and-sum (DAS) beamforming, its clinical application is limited by its sensitivity to phase aberrations. Several robust MV beamformers have been proposed, but present limitations when faced with second order phase aberration. Additionally, the information that can be obtained from phase aberration correction (PAC) methods is not utilized and the gain in robustness is usually accompanied by a loss in resolution or contrast. In the current work, we propose a new robust MV beamformer that uses a locally adaptive PAC (LAPAC-MV) in order to cope with the aformentioned difficulties. The method is based on a PAC estimation at every point in the image domain and a profile decision logic is included in the algorithm to take into account regions with low signal power. Preliminary results in full wave simulations and experimental phantom data are reported. In the resulting images, LAPAC-MV achieved enhancement in resolution of 0.03 mm, and reduction in sidelobe levels of around 8 dB when compared with precorrected DAS (DAS-PC) or precorrected MV (MV-PC). Contrast of LAPAC-MV is equivalent to MV-PC in cyst target simulations but the former showed improvements of approximately 1 dB in contrast in experiments with a 20 mm thick tissue aberrator.

In this study, a robust minimum variance beamformer (RMVB) is employed for source reconstruction in simultaneous MEG and local field potential (LFP) measurements. RMVB selects the electrical activity only from a specified volume of the brain while suppressing the rest. To improve imaging we added two more terms to the RMVB: the first term minimises the mean squared error (i.e. maximises the correlation) between the recorded LFP and reconstructed time courses from MEG data, the second term nulls the large inference induced by deep brain stimulation (DBS) device. A solution of this problem, relevant both with and without extra terms, is presented using the Lagrange multiplier method. This solution—if we ignore the new terms—has a simpler secular equation compared to its original solution and therefore is faster. The method is validated using both simulated and real data to show its potential use in practical applications.

Recently, robust minimum variance (MV) beamforming which optimizes the worst-case performance has been proposed in S.A. Vorobyov et al. (2003), R.G. Lorenz and S.P. Boyd (2005). The worst-case approach, however, might be overly conservative in practical applications. In this paper, we propose a more flexible approach that formulates the robust adaptive beamforming problem as a probability-constrained optimization problem with homogeneous quadratic cost function. Unlike the general probability-constrained problem which can be nonconvex and NP-hard, our problem can be reformulated as a convex nonlinear programming (NLP) problem, and efficiently solved using interior-point methods. Simulation results show an improved robustness of the proposed beamformer as compared to the existing state-of-the-art robust adaptive beamforming techniques

In order to solce the problem of lacking robustness against the unknown array steering vector in minimum variance beamformer. A new beamforming algorithm based on spherical uncertainty set is proposed in this paper. In this paper, we investigate the robust beamforming with spherical constraint on steering vector further and provide a novel robust minimum variance beamforming (RMVB) algorithm. Compared with existing methods in this field, the new algorithm is efficient in computation and more numerical stable.

In this paper, eyeblink artifacts of a multi-channel electroencephalogram (EEG) are extracted and removed by employing a spatial filter designed using the proposed efficient method via the robust minimum variance beamforming (RMVB). Unlike the conventional method where the spatial filter is designed using the correlation and prior knowledge of eyeblink from all channels of EEG, the spatial filter is obtained by simultaneously taking into consideration the local correlation and prior knowledge of each groups of EEG channels. The prior knowledge is obtained by taking into account the space-time-frequency information via the STF-TS model. Simulation results show that, by using less computational complexity, the proposed method can efficiently remove eyeblink artifacts from the multi-channel EEG as well as the conventional method.

In order to enhance the robustness and contrast in the minimum variance (MV) beamformer, adaptive diagonal loading method was proposed. The conventional diagonal loading technique has already been used in the MV beamformer, but has the drawback that its level is specified by predefined parameter and without consideration of input-data. To alleviate this problem, the level of diagonal loading was computed appropriately and automatically from the given data by shrinkage method in the proposed adaptive diagonal loaded beamformer. The performance of the proposed beamformer was tested on the simulated point target and cyst phantom was obtained using Field II. In the point target simulation, it is shown that the proposed method has higher lateral resolution than the conventional delay-and-sum beamformer and could be more robust in estimating the amplitude peak than the MV beamformer when acoustic velocity error exists. In the cyst phantom simulation, the proposed beamformer has shown that it achieves an improvement in contrast ratio and without distorting the edges of cyst.

A low-complexity and robust minimum variance beamformer for ultrasound imaging systems using beamspace dominant mode rejection

In this paper, a novel algorithm for transmit beamforming to single cochannel multicast group is presented. The problem of minimizing the total power transmitted by the antenna array subject to interference constraints at the primary receivers and quality-of-service (QoS) constraints at the secondary receivers is addressed. It is shown that this problem, which is nonconvex NP-hard, can be approximated by a convex second-order cone programming (SOCP) problem. Then, an iterative algorithm in which the SOCP approximation is successively refined is proposed. Simulation results show the superior performance of the proposed approach in terms of the total beamforming power, feasibility and computational complexity as compared to the existing ones1.

Minimum variance (MV) beamformers have been introduced in medical ultrasound imaging to improve image quality. In most cases, the MV beamformers have been investigated in terms of resolution improvement. However, the contrast-to-noise ratio (CNR) is also a clinically important metrics and gathers attention recently. In this study, we examined the diagonal loading parameter σ in MV beamforming and determined its appropriate value by evaluating image quality evaluation metrics including CNR. In order to further improve the image quality, a method for determining the value of σ based on the difference in statistical properties of received ultrasonic echo signals was also investigated. The phantom experimental results showed that the proposed method achieved a better CNR than the conventional MV beamformer while keeping resolution significantly better than that in delay-and-sum beamforming.

This paper considers the problem of high-resolution remote sensing (RS) of the environment formalized in the terms of a nonlinear ill-posed inverse problem of estimation of the power spatial spectrum pattern (SSP) of the wavefield scattered from an extended remotely sensed scene via processing the discrete measurements of a finite number of independent realizations of the observed degraded data signals [single realization of the trajectory signal in the case of synthetic aperture radar (SAR)]. We address a new descriptive experiment design regularization (DEDR) approach to treat the SSP reconstruction problem in the uncertain RS environment that unifies the paradigms of maximum likelihood nonparametric spectral estimation, descriptive experiment design, and worst case statistical performance optimization-based regularization. Pursuing such an approach, we establish a family of the DEDR-related SSP estimators that encompass a manifold of algorithms ranging from the traditional matched filter to the modified robust adaptive spatial filtering and minimum variance beamforming methods. The theoretical study is resumed with the development of a fixed-point iterative DEDR technique that incorporates the regularizing projections onto convex solution sets into the SSP reconstruction procedures to enforce the robustness and convergence. For the imaging SAR application, the proposed DEDR approach is aimed at performing, in a single optimized processing, adaptive SAR focusing, speckle reduction and RS scene image enhancement, and accounts for the possible presence of uncertain trajectory deviations.

In recent years, multiple-line acquisition (MLA) has been introduced to increase frame rate in cardiac ultrasound medical imaging. However, this method induces blocklike artifacts in the image. One approach suggested, synthetic transmit beamforming (STB), involves overlapping transmit beams which are then interpolated to remove the MLA blocking artifacts. Independently, the application of minimum variance (MV) beamforming has been suggested in the context of MLA. We demonstrate here that each approach is only a partial solution and that combining them provides a better result than applying either approach separately. This is demonstrated by using both simulated and real phantom data, as well as cardiac data. We also show that the STB-compensated MV beamfomer outperforms single-line acquisition (SLA) delay- and-sum in terms of lateral resolution.

GPU-Based Minimum Variance Beamformer for Synthetic Aperture Imaging of the Eye

Adaptive beamforming methods for ultrasound imaging have been studied to improve image resolution and contrast. The most common approach is the minimum variance (MV) beamformer which minimizes the power of the beamformed output while maintaining the response from the direction of interest constant. The method achieves higher resolution and better contrast than the delay-and-sum (DAS) beamformer, but it suffers from high computational cost. This cost is mainly due to the computation of the spatial covariance matrix and its inverse, which requires O(L(3)) computations, where L denotes the subarray size. In this study, we propose a computationally efficient MV beamformer based on QR decomposition. The idea behind our approach is to transform the spatial covariance matrix to be a scalar matrix σI and we subsequently obtain the apodization weights and the beamformed output without computing the matrix inverse. To do that, QR decomposition algorithm is used and also can be executed at low cost, and therefore, the computational complexity is reduced to O(L(2)). In addition, our approach is mathematically equivalent to the conventional MV beamformer, thereby showing the equivalent performances. The simulation and experimental results support the validity of our approach.

Recent research shows that non-convex AC OPF problem can be recast as a convex Semidefinite (SD) problem or Second Order Cone Programming (SOCP) problem. This paper presents a stochastic SOCP OPF (SSOCP-OPF) model for power systems connected to the wind farms. This is performed by reformulating the original non-convex OPF problem using more practical parameters of the power system. Finally, we obtain a convex optimization problem through some well-known approximations and an exact relaxation incorporating the stochastic nature of wind power. One of the advantage of convex SOCP problems, which are a general form of linear problems, is that they can be efficiently solved through Interior Point Methods (IPMs). The proposed OPF model takes advantage of both DC-OPF models (solution efficiency) and full AC-OPF models (solution accuracy). As an application of SSOCP-OPF model, we study the impact of wind power uncertainty on the transmission loss in the power systems. To evaluate the proposed stochastic model modified IEEE 30-bus test system is used. The optimization problem is coded in GAMS platform and solved using its embedded interior point optimizer MOSEK.

Recently, adaptive beamforming methods have been successfully applied to medical ultrasound imaging, resulting in significant improvement in image quality compared to non-adaptive delay-and-sum (DAS) beamformer. Most of the adaptive beamformers presented in the ultrasound imaging literature are based on the minimum variance (MV) beamformer which can improve the imaging resolution while retaining the contrast. The main objective of this research is to present a beamformer which could improve the imaging resolution and contrast, at the same time. In this paper, we have applied the eigenspace-based MV (EIBMV) beamformer to medical ultrasound imaging and shown the 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 obtained MV weight vector onto a vector subspace constructed from the eigenstructure of the covariance matrix. EIBMV beamformer shows a significant reduction in the sidelobe levels while representing the same mainlobe width as the MV. Specifically, in the point targets phantom, the proposed method decreases the sidelobes about 22 dB and 29 dB compared to MV and DAS, respectively. Furthermore, the proposed method increases the contrast of simulated cyst phantom about 8.6 dB and 14.1 dB and also improves the contrast-to-noise ratio about 31% and 61%, compared to MV and DAS, respectively.