Minimum Variance Beamformer Research Articles

Joint Adaptive Beamforming Techniques for Distributed Array Radars in Multiple Mainlobe and Sidelobe Jammings

In modern electronic warfare, array radar systems apply adaptive beamforming techniques to form nulls in the beams toward the jamming angles for multiple jamming cancellation. However, the nulls lead to distortion, especially within the mainlobe, which severely degrades the target detection ability. To address the degradation, this letter proposes joint adaptive beamforming techniques for distributed array radars by two-stage adaptive processing. First, the linearly constrained minimum variance beamforming is performed for multiple sidelobe jamming cancellation with mainlobe maintenance within each array radar. After that, joint beamspace processing with multiple radars is carried out for multiple mainlobe jamming cancellation using adaptive–adaptive algorithm. Excellent performance in both jamming cancellation and target detection is attained at very low computation and data transmission cost between multiple radar sites. Detailed evaluation and simulation results are provided to validate the proposed technique.

Integration of a Priori and Estimated Constraints Into an MVDR Beamformer for Speech Enhancement

Conventionally, the single constraint of the minimum variance distortionless response (MVDR) beamformer for speech enhancement has been defined using one of two approaches. Either it is based on a priori assumptions such as microphone characteristics, position, speech source location, and room acoustics, or on a relative transfer function (RTF) vector estimate using a data dependent method. Each approach has its respective merits and drawbacks and a decision usually has to be made between one of the approaches. In this paper, an alternative approach of using an integrated MVDR beamformer is investigated, where both the hard constraints from the two conventional approaches are softened to yield two tuning parameters. It will be shown that this integrated MVDR beamformer can be expressed as a convex combination of the conventional MVDR beamformers, a linearly constrained minimum variance (LCMV) beamformer, and an all-zero vector, with real, positive-valued coefficients. By analysing how the tuning parameters affect these coefficients, two tuning rules for a practical implementation of the integrated MVDR are subsequently proposed. An evaluation with simulated and recorded data demonstrates that the integrated MVDR beamformer can be beneficial as opposed to relying on either of the conventional MVDR beamformers.

Eigenspace-Based Minimum Variance Beamformer for Short-Lag Spatial Coherence Medical Ultrasound Imaging

Eigenspace-Based Minimum Variance Beamformer for Short-Lag Spatial Coherence Medical Ultrasound Imaging

Multiple constrained minimum variance beamformer (MCMV) performance in connectivity analyses

Functional brain connectivity is increasingly being seen as critical for cognition, perception and motor control. Magnetoencephalography and electroencephalography are modalities that offer noninvasive mapping of electrophysiological interactions among brain regions, yet suffer from signal leakage and signal cancellation when estimating brain activity. This leads to biased connectivity values which complicate interpretation. In this study, we test the hypothesis that a Multiple Constrained Minimum Variance beamformer (MCMV) outperforms the more traditional Linearly Constrained Minimum Variance beamformer (LCMV) for estimation of electrophysiological connectivity. To this end, MCMV and LCMV performance is compared in task related analyses with both simulated data and human MEG recordings of visual steady state signals, and in resting state analyses with simulated data and human MEG data of 89 subjects. In task related scenarios connectivity was estimated using coherence and phase locking values, whereas envelope correlations were used for the resting state data. We also introduce a novel Augmented Pairwise MCMV (APW-MCMV) approach for signal leakage suppression in resting state analyses and assess its performance against LCMV and more conventional MCMV approaches. We demonstrate that with MCMV effects of signal mixing and coherent source cancellation are greatly reduced in both task related and resting state conditions, while in contrast to other approaches 0- and short time lag interactions are preserved. In addition, we demonstrate that in resting state analyses, APW-MCMV strongly reduces spurious connections while better controlling for false negatives compared to more conservative measures such as symmetrical orthogonalization.

Harmonic beamformers for speech enhancement and dereverberation in the time domain

This paper presents a framework for parametric broadband beamforming that exploits the frequency-domain sparsity of voiced speech to achieve more noise reduction than traditional nonparametric broadband beamforming without introducing additional distortion. In this framework, the harmonic model is used to parametrize the signal of interest by a single parameter, the fundamental frequency, whereby both speech enhancement and derevereration can be performed. This framework thus exploits both the spatial and temporal properties of speech signals simultaneously and includes both fixed and adaptive beamformers, such as (1) delay-and-sum, (2) null forming, (3) Wiener, (4) minimum variance distortionless response (MVDR), and (5) linearly constrained minimum variance beamformers. Moreover, the framework contains standard broadband beamforming as a special case, whereby the proposed beamformers can also handle unvoiced speech. The reported experimental results demonstrate the capabilities of the proposed framework to perform both speech enhancement and dereverberation simultaneously. The proposed beamformers are evaluated in terms of speech distortion and objective measures for speech quality and speech intelligibility, and are compared to nonparametric broadband beamformers. The results show that the proposed beamformers perform well compared to traditional methods, including a state-of-the-art dereverberation method, particularly in adverse conditions with high amounts of noise and reverberation.

Robust matched field processing for array tilt and environmental mismatch

Adaptive matched field processing with the minimum variance beamformer provides excellent sidelobe suppression for source localization, but suffers from sensitivity to mismatch between the modeled and true acoustic field (i.e., environmental mismatch). To increase tolerance to the mismatch while retaining satisfactory sidelobe control, robust algorithms such as the white noise constraint (WNC) can be employed. The WNC alone, however, is not sufficient when the mismatch results from an unknown array tilt (i.e., geometric mismatch). This study introduces an adaptive matched field beamformer that is tolerant to both array tilt and environmental mismatch. By modeling the pressure fields corresponding to a set of assumed tilt angles, we impose multiple constraints that, when applied to the beamformer, increase robustness to the array tilt. Simulations and data results are presented to demonstrate localization and tracking of a surface ship (200–500 Hz) using a 16-element, 56-m long, tilted vertical array in approximately 100-m deep shallow water.

Low Complex Beam-Space Beamformer for Medical Ultrasound Imaging Based on Delay Multiply and Sum Method

The beam-space minimum variance (BSMV) beamforming is an outstanding form of beam-space beamforming. However, its computational complexity is still high for real-time ultrasound imaging. To solve this problem, a beamforming named beam-space delay multiply and sum (BS-DMAS) beamforming was proposed in this paper. In the proposed method, similar decimation discrete cosine transform (DCT) matrix in BSMV was used to reduce the dimension of signal firstly. Then, the improved delay multiply and sum (DMAS) beamforming in parallel form was used to get the final output. Different from BSMV, instead of calculating the inverse of covariance matrix to get the adaptive weight vector, the proposed method just need to perform square root, sign and addition operation. By doing this, the computational complexity was reduced from PM + P3 + 3P2 + O(P) to PM + P2 + O(P) compared with BSMV. Finally, simulation and experiment was performed to evaluate the proposed method. Compared with DAS, the results indicate that BS-DMAS generates a 66% lower advantage at full width at half-maximum (FWHM), an 114% improvement at contrast noise ratio (CR) but slightly worse at contrast ratio (CNR). This demonstrates that the proposed method can improve the performance of imaging and reduce the computational complexity.

A Robust Target Linearly Constrained Minimum Variance Beamformer With Spatial Cues Preservation for Binaural Hearing Aids

In this paper, a binaural beamforming algorithm for hearing aid applications is introduced.The beamforming algorithm is designed to be robust to some error in the estimate of the target speaker direction. The algorithm has two main components: a robust target linearly constrained minimum variance (TLCMV) algorithm based on imposing two constraints around the estimated direction of the target signal, and a post-processor to help with the preservation of binaural cues. The robust TLCMV provides a good level of noise reduction and low level of target distortion under realistic conditions. The post-processor enhances the beamformer abilities to preserve the binaural cues for both diffuse-like background noise and directional interferers (competing speakers), while keeping a good level of noise reduction. The introduced algorithm does not require knowledge or estimation of the directional interferers' directions nor the second-order statistics of noise-only components. The introduced algorithm requires an estimate of the target speaker direction, but it is designed to be robust to some deviation from the estimated direction. Compared with recently proposed state-of-the-art methods, comprehensive evaluations are performed under complex realistic acoustic scenarios generated in both anechoic and mildly reverberant environments, considering a mismatch between estimated and true sources direction of arrival. Mismatch between the anechoic propagation models used for the design of the beamformers and the mildly reverberant propagation models used to generate the simulated directional signals is also considered. The results illustrate the robustness of the proposed algorithm to such mismatches.

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

Minimum variance beamformer (MVB) has a high computational complexity that is mainly due to the inversion of an L×L covariance matrix involved during weight vector estimation, where L is the length of the subarray. In this work an attempt is made to reduce the computational complexity as well as increase the robustness against signal mismatch. The computational complexity is reduced by projecting the element-space data on to beamspace domain and then using dominant mode rejection on the beamspace covariance matrix (BCM). This reduces the dimension of covariance matrix and also eliminates the matrix inversion thereby reducing the computational complexity. Further, a closeness factor is introduced to determine the interference components that have to be suppressed, leading to increased robustness against signal mismatch. Performance of the proposed method has been evaluated on both simulated and experimental datasets. Results indicate that the proposed beamformer has a lateral resolution of 0.07 mm and a contrast resolution of 0.80, which are comparable to that of MVB which has a lateral and contrast resolution of 0.10 mm and 0.78, that too with a 12-fold reduction in computational complexity. The robustness of the peak magnitude estimate and spatial resolution of the beamformer with respect to error in estimation of sound velocity in the medium have also been evaluated. The variation in lateral resolution of proposed beamformer and MVB is approximately 1.21 mm and 1 mm. Further, the proposed beamformer has a maximum deviation in peak magnitude estimate of 0.7 dB whereas that of MVB is 2.5 dB, thus indicating the increased robustness of proposed method in peak magnitude estimate. Overall, the proposed beamformer has a 12-fold lower computational complexity compared to MVB with additional flexibility to increase the robustness against error in sound velocity.

A Sparsity-constraint Capon Beamforming Algorithm

In the presence of the steering vector of the signal of interest mismatches, nulls are formed in the direction of the signal of interest, which affects the performance of the beamforming. In this paper, a sparsity-constraint Capon beamforming based on iterative robust minimum variance beamforming is proposed. Using iteractive robust minimum variance beamforming, the mismatched steering vector is corrected. To achieve sidelobe level and suppress iterference, sparse constraints on beam response is added in the angel of sidelobe domain. Computer simulations have been conducted to verify validity and superiority of the proposed algorithm. It is shown that in the presence of mismatched steering vector, the proposed algorithm is more robust and has lower sidelobe level than the existing methods.

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.

Do the posterior midline cortices belong to the electrophysiological default-mode network?

The default-mode network (DMN) and its principal core hubs in the posterior midline cortices (PMC), i.e., the precuneus and the posterior cingulate cortex, play a critical role in the human brain structural and functional architecture. Because of their centrality, they are affected by a wide spectrum of brain disorders, e.g., Alzheimer's disease. Non-invasive electrophysiological techniques such as magnetoencephalography (MEG) are crucial to the investigation of the neurophysiology of the DMN and its alteration by brain disorders. However, MEG studies relying on band-limited power envelope correlation diverge in their ability to identify the PMC as a part of the DMN in healthy subjects at rest. Since these works were based on different MEG recording systems and different source reconstruction pipelines, we compared DMN functional connectivity estimated with two distinct MEG systems (Elekta, now MEGIN, and CTF) and two widely used reconstruction algorithms (Minimum Norm Estimation and linearly constrained minimum variance Beamformer). Our results identified the reconstruction method as the critical factor influencing PMC functional connectivity, which was significantly dampened by the Beamformer. On this basis, we recommend that future electrophysiological studies on the DMN should rely on Minimum Norm Estimation (or close variants) rather than on the classical Beamformer. Crucially, based on analytic knowledge about these two reconstruction algorithms, we demonstrated with simulations that this empirical observation could be explained by the existence of a spontaneous linear, approximately zero-lag synchronization structure between areas of the DMN or among multiple sources within the PMC. This finding highlights a novel property of the neural dynamics and functional architecture of a core human brain network at rest.

A new linearly constrained minimum variance beamformer for reconstructing EEG sparse sources

AbstractBrain source imaging based on EEG aims to reconstruct the neural activities producing the scalp potentials. This includes solving the forward and inverse problems. The aim of the inverse problem is to estimate the activity of the brain sources based on the measured data and leadfield matrix computed in the forward step. Spatial filtering, also known as beamforming, is an inverse method that reconstructs the time course of the source at a particular location by weighting and linearly combining the sensor data. In this paper, we considered a temporal assumption related to the time course of the source, namely sparsity, in the Linearly Constrained Minimum Variance (LCMV) beamformer. This assumption sounds reasonable since not all brain sources are active all the time such as epileptic spikes and also some experimental protocols such as electrical stimulations of a peripheral nerve can be sparse in time. Developing the sparse beamformer is done by incorporating L1‐norm regularization of the beamformer output in the relevant cost function while obtaining the filter weights. We called this new beamformer SParse LCMV (SP‐LCMV). We compared the performance of the SP‐LCMV with that of LCMV for both superficial and deep sources with different amplitudes using synthetic EEG signals. Also, we compared them in localization and reconstruction of sources underlying electric median nerve stimulation. Results show that the proposed sparse beamformer can enhance reconstruction of sparse sources especially in the case of sources with high amplitude spikes.

Estimating neural sources using a worst-case robust adaptive beamforming approach

Recently, brain source localization and beamforming methods have played an important role in enhancing the utility of the electroencephalograph (EEG) and/or the magnetoencephalograph (MEG). Source localization methods are in general very sensitive to parameter values used to describe the underlying lead–field matrix, such as head shape, electrode positions, conductivity of various tissues of the head, etc. Errors in these parameter values can cause significant degradation in performance of these algorithms.In this paper, we develop a robust minimum variance beamformer (RMVB) specifically for EEG applications that can deal with an arbitrary mismatch between the assumed and true lead field matrix. The approach optimizes the worst-case uncertainty performance, sacrificing a distortionless response in exchange for more robust performance. The performance of the RMVB is compared with the classic minimum variance beamformer (MVB) as well as its regularized and eigenspace-based variations. The simulation scenarios highlight the superior ability of the RMVB to cope with arbitrary mismatches.

Distributed Rate-Constrained LCMV Beamforming

In this letter, we propose a decentralized framework for rate-distributed linearly constrained minimum variance (LCMV) beamforming in wireless acoustic sensor networks. To save the energy usage within the network, we propose to minimize the transmission cost and put a constraint on the noise reduction performance. Subsequently, we decentralize the obtained LCMV filter structure by exploiting an imposed block diagonal form of the noise correlation matrix. As a result, the beamformer weights are calculated in a decentralized fashion and each node can determine its quantization rate locally. Finally, numerical results validate the proposed method.

The impact of improved MEG–MRI co-registration on MEG connectivity analysis

Co-registration between structural head images and functional MEG data is needed for anatomically-informed MEG data analysis. Despite the efforts to minimize the co-registration error, conventional landmark- and surface-based strategies for co-registering head and MEG device coordinates achieve an accuracy of typically 5–10 mm. Recent advances in instrumentation and technical solutions, such as the development of hybrid ultra-low-field (ULF) MRI–MEG devices or the use of 3D-printed individualized foam head-casts, promise unprecedented co-registration accuracy, i.e., 2 mm or better. In the present study, we assess through simulations the impact of such an improved co-registration on MEG connectivity analysis.We generated synthetic MEG recordings for pairs of connected cortical sources with variable locations. We then assessed the capability to reconstruct source-level connectivity from these recordings for 0–15-mm co-registration error, three levels of head modeling detail (one-, three- and four-compartment models), two source estimation techniques (linearly constrained minimum-variance beamforming and minimum-norm estimation MNE) and five separate connectivity metrics (imaginary coherency, phase-locking value, amplitude-envelope correlation, phase-slope index and frequency-domain Granger causality).We found that beamforming can better take advantage of an accurate co-registration than MNE. Specifically, when the co-registration error was smaller than 3 mm, the relative error in connectivity estimates was down to one-third of that observed with typical co-registration errors. MNE provided stable results for a wide range of co-registration errors, while the performance of beamforming rapidly degraded as the co-registration error increased. Furthermore, we found that even moderate co-registration errors (>6 mm, on average) essentially decrease the difference of four- and three- or one-compartment models. Hence, a precise co-registration is important if one wants to take full advantage of highly accurate head models for connectivity analysis.We conclude that an improved co-registration will be beneficial for reliable connectivity analysis and effective use of highly accurate head models in future MEG connectivity studies.

Short-lag spatial coherence imaging using minimum variance beamforming on dual apertures

BackgroundShort-lag spatial coherence (SLSC) imaging, a newly proposed ultrasound imaging scheme, can offer a higher lesion detectability than conventional B-mode imaging. It requires a high focusing quality which can be satisfied by the synthetic aperture imaging mode. However, traditional nonadaptive synthesis for the SLSC still offers an unsatisfactory resolution. The spatial coherence estimation on the receive aperture cannot fully utilize the coherence information in two-dimensional (2D) echo data.MethodsTo overcome these drawbacks, an improved SLSC scheme with adaptive synthesis on dual apertures is proposed in this paper. The minimum variance (MV) beamformer is applied in synthesizing both the receiving and transmitting apertures, while the SLSC function is estimated on both apertures as well. In this way, the resolution is enhanced by the MV implementation, while the coherence in dual apertures is fully utilized.ResultsSimulations, phantom experiments, and in vivo studies are conducted to evaluate the performance of the proposed method. Results demonstrate that the proposed method achieves the best performance in terms of the contrast ratio (CR), contrast-to-noise ratio (CNR), and the speckle signal-to-noise ratio (SNR). Specifically, compared with the delay-and-sum (DAS) method, the proposed method achieves 42.5% higher CR, 412.7% higher CNR, and 402.9% higher speckle SNR in simulations. The resolution is also better than the DAS and conventional SLSC beamformers.ConclusionsThe proposed method is a promising technique for improving the SLSC imaging quality and can provide better visualization for medical diagnosis.

Quantifying the Effect of Demixing Approaches on Directed Connectivity Estimated Between Reconstructed EEG Sources.

Electrical activity recorded on the scalp using electroencephalography (EEG) results from the mixing of signals originating from different regions of the brain as well as from artifactual sources. In order to investigate the role of distinct brain areas in a given experiment, the signal recorded on the sensors is typically projected back into the brain (source reconstruction) using algorithms that address the so-called EEG "inverse problem". Once the activity of sources located inside of the brain has been reconstructed, it is often desirable to study the statistical dependencies among them, in particular to quantify directional dynamical interactions between brain areas. Unfortunately, even when performing source reconstruction, the superposition of signals that is due to the propagation of activity from sources to sensors cannot be completely undone, resulting in potentially biased estimates of directional functional connectivity. Here we perform a set of simulations involving interacting sources to quantify source connectivity estimation performance as a function of the location of the sources, their distance to each other, the noise level, the source reconstruction algorithm, and the connectivity estimator. The generated source activity was projected onto the scalp and projected back to the cortical level using two source reconstruction algorithms, linearly constrained minimum variance beamforming and 'Exact' low-resolution tomography (eLORETA). In source space, directed connectivity was estimated using multi-variate Granger causality and time-reversed Granger causality, and compared with the imposed ground truth. Our results demonstrate that all considered factors significantly affect the connectivity estimation performance.

MEG Source Imaging and Group Analysis Using VBMEG.

Variational Bayesian Multimodal EncephaloGraphy (VBMEG) is a MATLAB toolbox that estimates distributed source currents from magnetoencephalography (MEG)/electroencephalography (EEG) data by integrating functional MRI (fMRI) (https://vbmeg.atr.jp/). VBMEG also estimates whole-brain connectome dynamics using anatomical connectivity derived from a diffusion MRI (dMRI). In this paper, we introduce the VBMEG toolbox and demonstrate its usefulness. By collaborating with VBMEG's tutorial page (https://vbmeg.atr.jp/docs/v2/static/vbmeg2_tutorial_neuromag.html), we show its full pipeline using an open dataset recorded by Wakeman and Henson (2015). We import the MEG data and preprocess them to estimate the source currents. From the estimated source currents, we perform a group analysis and examine the differences of current amplitudes between conditions by controlling the false discovery rate (FDR), which yields results consistent with previous studies. We highlight VBMEG's characteristics by comparing these results with those obtained by other source imaging methods: weighted minimum norm estimate (wMNE), dynamic statistical parametric mapping (dSPM), and linearly constrained minimum variance (LCMV) beamformer. We also estimate source currents from the EEG data and the whole-brain connectome dynamics from the MEG data and dMRI. The observed results indicate the reliability, characteristics, and usefulness of VBMEG.

Fast adaptive beamforming through a cascade structure for ultrasound imaging.

A major limiting factor for applying a minimum variance (MV) beamformer in medical ultrasound imaging is its high computational complexity. This paper introduces a new fast MV beamforming method with almost the same capabilities as the standard MV. The fast beamformer is implemented using a cascade structure. At the first stage, the echo signals received from the points far from the main axis are strongly suppressed using a fixed-weight beamformer. At the second stage, after spatially decimating the output of the first stage, an MV-based adaptive beamformer is used to eliminate the echo signals from the points adjacent to the focal point. The greatest advantage of the proposed method is that the second beamformer can be a low-complexity implementation of MV such as beamspace (BS) MV to further reduce the complexity, resulting in a superfast MV. The resulting beamformers were evaluated through both simulation and experimental data, and it was verified that the method was competitive with standard MV and BS methods at a lower computational cost. The new fast and superfast MV methods are capable of obtaining the same results as the MV and BS-MV, at a significantly lower computational cost.