A Low-complexity Minimum-variance Beamformer Based on Orthogonal Decomposition of the Compounded Subspace.

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.

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.

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.

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

Beamforming (BF) in ultrasound (US) imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum (DAS) is still extensively used nowadays in clinical applications, due to its real-time capabilities. The most common alternatives are minimum variance (MV) method and its variants, which overcome the drawbacks of DAS, at the cost of higher computational complexity that limits its utilization in real-time applications. In this paper, we propose to perform BF in US imaging through a regularized inverse problem based on a linear model relating the reflected echoes to the signal to be recovered. Our approach presents two major advantages: 1) its flexibility in the choice of statistical assumptions on the signal to be beamformed (Laplacian and Gaussian statistics are tested herein) and 2) its robustness to a reduced number of pulse emissions. The proposed framework is flexible and allows for choosing the right tradeoff between noise suppression and sharpness of the resulted image. We illustrate the performance of our approach on both simulated and experimental data, with in vivo examples of carotid and thyroid. Compared with DAS, MV, and two other recently published BF techniques, our method offers better spatial resolution, respectively contrast, when using Laplacian and Gaussian priors.

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.

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

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 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.

Ultrafast Plane Wave Imaging Using Tensor Completion-Based Minimum Variance Algorithm.

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.

The major problem in adaptively processing data from a large array is inversion of the covariance matrix. The matrix must be well-conditioned to be inverted. The number of independent samples that is needed to form a well-conditioned matrix is at least twice the number of array elements. The integration time to form a well-conditioned large array covariance matrix may then be unreasonably long relative to the coherent time of signal in a changing environment. A sub-optimal subarray processing has been developed. The adaptive weight vectors are calculated for each subarray. These weight vectors are linearly combined to form a full-array adaptive weight vector and are applied to the full-array covariance matrix. The required integration time is reduced to that which is needed to form the well-conditioned subarray covariance matrices. In a recent shallow water experiment, a three-dimensional array had been deployed. The array consisted of 5 VLAs each with 30-element spaced evenly on a circular baseline of a radius of 200 m. The subarray processing approach had been used to localize a moving source that had a fast range/bearing change relative to the baseline.

In medical ultrasound B-mode imaging, by increasing the image contrast, spatial and temporal resolution, it will help to improve the diagnostic and decision making process. Previously the unsharp masking (UM) techniques have been successfully implemented for digital image processing as edge enhancement techniques. However, the outcomes of the method are limited and influenced by the image formats conversion and lower dynamic range. Moreover the conventional UM technique sensitive to noise due to the presence of linear high pass filter which cannot discriminate signal from noise. Furthermore, the technique only enhances the image in darker compared to lighter regions. To overcome those issues, a new improved UM method compatible with ultrasound B-mode imaging was applied to compound plane wave imaging (CPWI). The received radio frequency (RF) signal was beamformed with delay and sum (DAS) and filtered delay and sum (FDMAS). Results show that the proposed techniques are not only able to improve the image contrast but also the spatial resolution. The UM technique manages to improve the B-mode image lateral resolution (LR) by 18.36% and 10.25% as well as reduced the peak side lobes (PSL) by 16.67 dB and 21.24 dB on DAS and FDMAS respectively when compounded with CPWI, N=13. For the same number of compounding and beamforming order, the image contrast ratio (CR) has been improved by 10.35 dB and 7.39 dB accordingly.