Robust minimum variance beamformer using locally adaptive phase aberration correction

An interesting relationship between the probability-constrained and worst-case optimization based robust minimum variance (MV) beamformers has been discovered. It is shown that both in the cases of circularly symmetric Gaussian and worst-case distributions of the steering vector mismatch, the probability-constrained robust MV beamforming problem can be tightly approximated as a convex second-order cone programming (SOCP) problem. The latter problem is mathematically equivalent to that resulting from the deterministic worst-case approach and, therefore, probability-constrained beamformers can be interpreted and implemented using their deterministic worst-case counterparts. However, an important advantage of the developed probability-constrained MV beamformers with respect to their standard worst-case counterparts is that the former approaches enable to explicitly quantify the parameters of the uncertainty region in terms of the beamformer outage probability.

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.

In this paper, the adaptive, minimum variance (MV) beam-former is applied to medical ultrasound imaging. The significant resolution and contrast gain provided by the adaptive, minimum variance (MV) beamformer, introduces the possibility of plane wave (PW) ultrasound imaging. Data is obtained using Field II and a 7 MHz, 128-elements, linear array transducer with lambda/2-spacing. MV is compared to the conventional delay-and-sum (DS) beamformer with Boxcar and Hanning weights. Furthermore, the PW images are compared to the a conventional ultrasound image, obtained from a linear scan sequence. The four approaches, {Linear Scan, DS Boxcar, DS Hanning, MV}, have full width at half maximum of {0.82, 0.71, 1.28, 0.12} mm and peak side-lobe levels of {-40.1,-16.8,-34.4,-57.0} dB.

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.

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.

In the recent years, various studies have been performed on adaptive beamforming especially for medical ultrasound imaging. In this paper, at first we applied the adaptive Minimum Variance (MV) beamforming to the simulated data derived from Field II. In contrast to conventional beamforming (DAS), MV adaptive beamforming can significantly improve the imaging resolution while retaining the contrast of the image. Then we combined MV with Coherence Factor (CF), by which the resolution and contrast of the medical ultrasound images are simultaneously increased. We implemented these beamformers in the MATLAB and survey the authenticity of them, then fulfil the beamformers with the Visual Studio codes. Those had the same results but execution times of Visual Studio codes are about 13 times lower than other. The major parameters which affect on the image quality are number of elements, height of elements, and sampling frequency. We investigated the effect of these parameters on the image quality by some simulated examples. The results illustrated that the reduction of the number of elements from M=96 to 24 and sampling frequency from 100MHz to 20MHz will degrade quality of the images. Nevertheless, the results of MV beamformer with M=24 and Fs=20MHz are comparable to DAS with M=96 and Fs=100MHz. We illustrated that if height of elements is equal or greater than 5mm, the off-plane targets have a negligible effect on the image quality but if the height of elements is in the same order of the width the off-plane targets have a significant role on the image quality. It should be taken into consideration in using of planar probs.

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.

The pulse-echo technique has been widely used in medical ultrasound imaging. This technique uses an array of transducer elements to transmit a focused beam into the body, and each element then becomes a receiver to collect the echoes. The received echoes from each element are dynamically focused to form an image. Focusing on transmission and reception is performed assuming that the wave propagation speed inside the body is the same everywhere. Unfortunately, the speed inside the body is not constant; it varies from 1470 m/s to greater than 1600 m/s. This speed variation will result in increased side lobes and degraded lateral resolution. Aberration phenomena and their extent in tissue have been evaluated in many works (O'Donnell & Flax 1988; Zhu & Steinberg, 1992; Shmulewitz et al., 1993; Robinson et al., 1994; Hinkelman et al., 1998). The degradation might be tolerable if the frequency is not very high and the aperture size of the array is not very large. However, higher frequencies and larger apertures have been used to improve lateral resolution of ultrasound images. But the resolution improvement cannot be achieved beyond a certain limit, because both larger aperture and higher frequency make the system more sensitive to propagation velocity variations in the body. For example, the four transverse abdominal scan images shown in the first row of Fig.1 were formed with a 64-element linear array using four different aperture sizes (9 mm, 12 mm, 18 mm, and 27 mm) to form each single beam in the image. The array pitch was 1.0 mm and the pulse had a 3.5 MHz centre frequency and 2 MHz bandwidth. The Superior-Mesenteric-Artery (SMA) and the Aorta (A) are the main objects in these images. Because of the shape of the rectus muscles (speed ~ 1580 m/s) and the fat layers (speed ~ 1450 m/s) at this position, the distortions caused by phase aberration in these images can be easily seen. In the 9-mm aperture image, the superior-mesenteric-artery is almost doubled but the artery wall can still be recognized. When the aperture size becomes larger, the distortion becomes worse. Phase aberration is one of the most important factors that limit improvement to lateral resolution of ultrasound imaging systems. Successful correction of phase aberrations will make it possible to improve the lateral resolution of images. Phase aberration corrected images using the near-field-signal-redundancy algorithm (Li, 1997) are shown in the second row of Fig.1 and the lateral resolution is improved when the aperture size becomes larger. In this chapter, the near-field-signal-redundancy algorithm is described in details. But first, a review of some related methods developed for phase-aberration correction is given. The

Phase aberration correction for ultrasound imaging guided extracorporeal shock wave therapy (ESWT): Feasibility study

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.

Constraint matrix projection minimum variance beamformer based on adaptive decomposition threshold for ultrasound imaging

In the article "Effect of element directivity on adaptive beamforming applied to high-frame-rate ultrasound" [ibid., vol. 62, no. 3, pp. 511-523, 2015], the contrast C was correctly defined. The authors note that therefore, 20 log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> 4 = 12.04 dB should be added to all the contrast values in the paper to obtain the correct contrast values.

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 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.

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.