A low-complexity adaptive beamformer for ultrasound imaging using structured covariance matrix

In recent years, adaptive beamforming methods have been successfully applied to medical ultrasound imaging, resulting in simultaneous improvement in imaging resolution and contrast. These improvements have been achieved at the expense of higher computational complexity, with respect to the conventional non-adaptive delay-and-sum (DAS) beamformer, in which computational complexity is proportional to the number of elements, O(M). The computational overhead results from the covariance matrix inversion needed for computation of the adaptive weights, the complexity of which is cubic with the subarray size, O(L(3)). This is a computationally intensive procedure, which makes the implementation of adaptive beamformers less attractive in spite of their advantages. Considering that, in medical ultrasound applications, most of the energy is scattered from angles close to the steering angle, assuming spatial stationarity is a good approximation, allowing us to assume the Toeplitz structure for the estimated covariance matrix. Based on this idea, in this paper, we have applied the Toeplitz structure to the spatially smoothed covariance matrix by averaging the entries along all subdiagonals. Because the inverse of the resulting Toeplitz covariance matrix can be computed in O(L(2)) operations, this technique results in a greatly reduced computational complexity. By using simulated and experimental RF data-point targets as well as cyst phantoms-we show that the proposed low-complexity adaptive beamformer significantly outperforms the DAS and its performance is comparable to that of the minimum variance beamformer, with reduced computational complexity.     

抑制运动强干扰的稳健波束域目标方位估计方法

为了减小来自旁瓣区快速运动的强干扰对波束域高分辨方位估计方法的影响,提出一种稳健的波束域高分辨方位估计方法。该方法在形成多波束时,将稳健自适应波束形成与零陷扩宽技术相结合,有效地抑制了运动强干扰所造成的快拍失效和扫描方向误差引起的自适应波束图畸变,从而保证波束域方法能准确地估计目标方位。仿真结果验证了该方法的有效性。     

Capon beamforming in medical ultrasound imaging with focused beams

Medical ultrasound imaging is conventionally done by insonifying the imaged medium with focused beams. The backscattered echoes are beamformed using delay-and-sum operations that cannot completely eliminate the contribution of signals backscattered by structures off the imaging beam to the beamsum. It leads to images with limited resolution and contrast. This paper presents an adaptation of the Capon beamformer algorithm to ultrasound medical imaging with focused beams. The strategy is to apply data-dependent weight functions to the imaging aperture. These weights act as lateral spatial filters that filter out off-axis signals. The weights are computed for each point in the imaged medium, from the statistical analysis of the signals backscattered by that point to the different elements of the imaging probe when insonifying it with different focused beams. Phantom and in vivo images are presented to illustrate the benefits of the Capon algorithm over the conventional delay and-sum approach. On heart sector images, the clutter in the heart chambers is decreased. The endocardium border is better defined. On abdominal linear array images, significant contrast and resolution enhancement are observed.     

An approach to multibeam covariance matrices for adaptive beamforming in ultrasonography

Medical ultrasound imaging systems are often based on transmitting, and recording the backscatter from, a series of focused broadband beams with overlapping coverage areas. When applying adaptive beamforming, a separate array covariance matrix for each image sample is usually formed. The data used to estimate any one of these covariance matrices is often limited to the recorded backscatter from a single transmitted beam, or that of some adjacent beams through additional focusing at reception. We propose to form, for each radial distance, a single covariance matrix covering all of the beams. The covariance matrix is estimated by combining the array samples after a sequenced time delay and phase shift. The time delay is identical to that performed in conventional delay-and-sum beamforming. The performance of the proposed approach in conjunction with the Capon beamformer is studied on both simulated data of scenes consisting of point targets and recorded ultrasound phantom data from a specially adapted commercial scanner. The results show that the proposed approach is more capable of resolving point targets and gives better defined cyst-like structures in speckle images compared with the conventional delay-and-sum approach. Furthermore, it shows both an increased robustness to noise and an increased ability to resolve point-like targets compared with the more traditional per-beam Capon beamformer.     

Contrast enhancement and robustness improvement of adaptive ultrasound imaging using forward-backward minimum variance beamforming

In adaptive ultrasound imaging, accurate estimation of the array covariance matrix is of great importance, and biases the performance of the adaptive beamformer. The more accurately the covariance matrix can be estimated, the better the resolution and contrast can be achieved in the ultrasound image. To this end, in this paper, we have used the forward-backward spatial averaging for array covariance matrix estimation, which is then employed in minimum variance (MV) weights calculation. The performance of the proposed forward-backward MV (FBMV) beamformer is tested on simulated data obtained using Field II. Data for two closely located point targets surrounded by speckle pattern are simulated showing the higher amplitude resolution of the FBMV beamformer in comparison to the forward-only (F-only) MV beamformers, without the need for diagonal loading. A circular cyst with a diameter of 6 mm and a phantom containing wire targets and two cysts with different diameters of 8 mm and 6 mm are also simulated. The simulations show that the FBMV beamformer, in contrast to the F-only MV, could estimate the background speckle statistics without the need for temporal smoothing, resulting in higher contrast for the FBMV-resulted image in comparison to the MV images. In addition, the effect of steering vector errors is investigated by applying an error of the sound speed estimate to the ultrasound data. The simulations show that the proposed FBMV beamformer presents a satisfactory robustness against data misalignment resulted from steering vector errors, outperforming the regularized F-only MV beamformer. These improvements are achieved without compromising the good resolution of the MV beamformer and resulted from more accurate estimation of the covariance matrix and consequently, the more accurate setting of the MV weights.     

Eigenspace-based minimum variance beamforming applied to medical ultrasound imaging

Recently, adaptive beamforming methods have been successfully applied to medical ultrasound imaging, resulting in significant improvement in image quality compared with non-adaptive delay-and-sum (DAS) beamformers. Most of the adaptive beamformers presented in the ultrasound imaging literature are based on the minimum variance (MV) beamformer which can significantly improve the imaging resolution, although their success in enhancing the contrast has not yet been satisfactory. It is desirable for the beamformer to improve the resolution and contrast at the same time. To this end, in this paper, we have applied the eigenspace-based MV (EIBMV) beamformer to medical ultrasound imaging and have shown a 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 MV weight vector onto a vector subspace constructed from the eigenstructure of the covariance matrix. Using EIBMV weights instead of the MV ones leads to reduced sidelobes and improved contrast, without compromising the high resolution of the MV beamformer. In addition, the proposed EIBMV beamformer presents a satisfactory robustness against data misalignment resulting from steering vector errors, outperforming the regularized MV beamformer.     

A low-complexity data-dependent beamformer

The classical problem of choosing apodization functions for a beamformer involves a trade-off between main lobe width and side lobe level, i.e., a trade-off between resolution and contrast. To avoid this trade-off, the application of adaptive beamforming, such as minimum variance beamforming, to medical ultrasound imaging has been suggested. This has been an active topic of research in medical ultrasound imaging in the recent years, and several authors have demonstrated significant improvements in image resolution. However, the improvement comes at a considerable cost. Where the complexity of a conventional beamformer is linear with the number of elements [O(M)], the complexity of a minimum variance beamformer is as high as O(M3). In this paper, we have applied a method based on an idea by Vignon and Burcher which is data-adaptive, but selects the apodization function between several predefined windows, giving linear complexity. In the proposed method, we select an apodization function for each depth along a scan line based on the optimality criterion of the minimum variance beamformer. However, unlike the minimum variance beamformer, which has an infinite solution space, we limit the number of possible outcomes to a set of predefined windows. The complexity of the method is then only P times that of the conventional method, where P is the number of predefined windows. The suggested method gives significant improvement in image resolution at a low cost. The method is robust, can handle coherent targets, and is easy to implement. It may also be used as a classifier because the selected window gives information about the object being imaged. We have applied the method to simulated data of wire targets and a cyst phantom, and to experimental RF data from a heart phantom using P = 4 and P = 12. The results show significant improvement in image resolution compared with delay-and-sum.     

Adaptive beamforming applied to medical ultrasound imaging

We have applied the minimum variance (MV) adaptive beamformer to medical ultrasound imaging and shown significant improvement in image quality compared to delay-and-sum (DAS). We demonstrate reduced mainlobe width and suppression of sidelobes on both simulated and experimental RF data of closely spaced wire targets, which gives potential contrast and resolution enhancement in medical images. The method is applied to experimental RF data from a heart phantom, in which we show increased resolution and improved definition of the ventricular walls. A potential weakness of adaptive beamformers is sensitivity to errors in the assumed wavefield parameters. We look at two ways to increase robustness of the proposed method; spatial smoothing and diagonal loading. We show that both are controlled by a single parameter that can move the performance from that of a MV beamformer to that of a DAS beamformer. We evaluate the sensitivity to velocity errors and show that reliable amplitude estimates are achieved while the mainlobe width and sidelobe levels are still significantly lower than for the conventional beamformer.     

空域预滤波的稳健自适应波束形成方法

假定的期望信号方向向量与真实信号方向向量存在误差时,常规自适应波束形成性能将严重降低,针对该问题,提出了一种稳健的自适应波束形成算法.首先利用凹槽空域矩阵滤波器对基阵接收数据进行空域预滤波,消除协方差矩阵中的期望信号分量,然后重构协方差矩阵同时反变换到阵元域,再用重构的协方差矩阵形成自适应波束权向量.由于方法消除了期望信号分量的影响,极大地提高了自适应波束形成算法对系统误差的稳健性.计算机仿真验证了所提方法的有效性.     

Benefits of Minimum-Variance Beamforming in Medical Ultrasound Imaging

Recently, significant improvement in image resolution has been demonstrated by applying adaptive beamforming to medical ultrasound imaging. In this paper, we have used the minimum-variance beamformer to show how the low sidelobe levels and narrow beamwidth of adaptive methods can be used, not only to increase resolution, but also to enhance imaging in several ways. By using a minimum-variance beamformer instead of delay-and-sum on reception, reduced aperture, higher frame rates, or increased depth of penetration can be achieved without sacrificing image quality. We demonstrate comparable resolution on images of wire targets and a cyst phantom obtained with a 96-element, 18.5-mm transducer using delay-and-sum, and a 48-element, 9.25-mm transducer using minimum variance. To increase frame rate, fewer and wider transmit beams in combination with several parallel receive beams may be used. We show comparable resolution to delay-and-sum using minimum variance, 1/4th of the number of transmit beams and 4 parallel receive beams, potentially increasing the frame rate by 4. Finally, we show that by lowering the frequency of the transmitted beam and beamforming the received data with the minimum variance beamformer, increased depth of penetration is achieved without sacrificing lateral resolution.     

Spatio-temporal operator formalism for holographic recording and diffraction in a photorefractive-based true-time-delay phased-array processor

We present a spatio-temporal operator formalism and beam propagation simulations that describe the broadband efficient adaptive method for a true-time-delay array processing (BEAMTAP) algorithm for an optical beamformer by use of a photorefractive crystal. The optical system consists of a tapped-delay line implemented with an acoustooptic Bragg cell, an accumulating scrolling time-delay detector achieved with a traveling-fringes detector, and a photorefractive crystal to store the adaptive spatio-temporal weights as volume holographic gratings. In this analysis, linear shift-invariant integral operators are used to describe the propagation, interference, grating accumulation, and volume holographic diffraction of the spatio-temporally modulated optical fields in the system to compute the adaptive array processing operation. In addition, it is shown that the random fluctuation in time and phase delays of the optically modulated and transmitted array signals produced by fiber perturbations (temperature fluctuations, vibrations, or bending) are dynamically compensated for through the process of holographic wavefront reconstruction as a byproduct of the adaptive beam-forming and jammer-excision operation. The complexity of the cascaded spatial-temporal integrals describing the holographic formation, and subsequent readout processes, is shown to collapse to a simple imaging condition through standard operator manipulation. We also present spatio-temporal beam propagation simulation results as an illustrative demonstration of our analysis and the operation of a BEAMTAP beamformer.     

An integrated circuit with transmit beamforming flip-chip bonded to a 2-D CMUT array for 3-D ultrasound imaging

State-of-the-art 3-D medical ultrasound imaging requires transmitting and receiving ultrasound using a 2-D array of ultrasound transducers with hundreds or thousands of elements. A tight combination of the transducer array with integrated circuitry eliminates bulky cables connecting the elements of the transducer array to a separate system of electronics. Furthermore, preamplifiers located close to the array can lead to improved receive sensitivity. A combined IC and transducer array can lead to a portable, high-performance, and inexpensive 3-D ultrasound imaging system. This paper presents an IC flip-chip bonded to a 16 x 16-element capacitive micromachined ultrasonic transducer (CMUT) array for 3-D ultrasound imaging. The IC includes a transmit beamformer that generates 25-V unipolar pulses with programmable focusing delays to 224 of the 256 transducer elements. One-shot circuits allow adjustment of the pulse widths for different ultrasound transducer center frequencies. For receiving reflected ultrasound signals, the IC uses the 32-elements along the array diagonals. The IC provides each receiving element with a low-noise 25-MHz-bandwidth transimpedance amplifier. Using a field-programmable gate array (FPGA) clocked at 100 MHz to operate the IC, the IC generated properly timed transmit pulses with 5-ns accuracy. With the IC flip-chip bonded to a CMUT array, we show that the IC can produce steered and focused ultrasound beams. We present 2-D and 3-D images of a wire phantom and 2-D orthogonal cross-sectional images (Bscans) of a latex heart phantom.     

Minimum Variance Beamforming Combined with Adaptive Coherence Weighting Applied to Medical Ultrasound Imaging

Currently, the nonadaptive delay-and-sum (DAS) beamformer is used in medical ultrasound imaging. However, due to its data-independent nature, DAS leads to images with limited resolution and contrast. In this paper, an adaptive minimum variance (MV)-based beamformer that combines the MV and coherence factor (CF) weighting is introduced and adapted to medical ultrasound imaging. MV-adaptive beamformers can improve the image quality in terms of resolution and sidelobes by suppressing off-axis signals, while keeping onaxis ones. In addition, CF weighting can improve contrast and sidelobes by emphasizing the in-phase signals and reducing the out-of-phase ones. Combining MV and CF weighting results in simultaneous improvement of imaging resolution and contrast, outperforming both DAS and MV beamformers. In addition, because of the power of CF in reducing the focusing errors, the proposed method presents satisfactory robustness against sound velocity inhomogeneities, outperforming the regularized MV beamformer. The excellent performance of the proposed beamforming approach is demonstrated by several simulated examples.     

基于二阶锥规划的稳健低旁瓣自适应波束形成

针对水下成像时圆弧阵常规波束旁瓣级较高,当存在强干扰时容易带来较多虚警的缺点,提出一种基于二阶锥规划的稳健低旁瓣自适应波束形成方法。该方法通过对波束旁瓣进行优化设计,可以将波束旁瓣级进行严格控制,并进一步结合协方差矩阵重构法,使波束形成器的稳健性得到提高,最后将该波束优化问题转化为二阶锥规划问题进行求解。计算机仿真结果表明,相较于其他算法来说,文中算法在波束旁瓣级得到严格控制的同时,可以在存在各类失配的情况下获得更高的输出信干噪比,稳健性更高。水池实验进一步验证了该方法的有效性,该研究成果可以在声呐成像领域应用。     

GPU-based beamformer: fast realization of plane wave compounding and synthetic aperture imaging

Although they show potential to improve ultrasound image quality, plane wave (PW) compounding and synthetic aperture (SA) imaging are computationally demanding and are known to be challenging to implement in real-time. In this work, we have developed a novel beamformer architecture with the real-time parallel processing capacity needed to enable fast realization of PW compounding and SA imaging. The beamformer hardware comprises an array of graphics processing units (GPUs) that are hosted within the same computer workstation. Their parallel computational resources are controlled by a pixel-based software processor that includes the operations of analytic signal conversion, delay-and-sum beamforming, and recursive compounding as required to generate images from the channel-domain data samples acquired using PW compounding and SA imaging principles. When using two GTX-480 GPUs for beamforming and one GTX-470 GPU for recursive compounding, the beamformer can compute compounded 512 x 255 pixel PW and SA images at throughputs of over 4700 fps and 3000 fps, respectively, for imaging depths of 5 cm and 15 cm (32 receive channels, 40 MHz sampling rate). Its processing capacity can be further increased if additional GPUs or more advanced models of GPU are used.     

A single FPGA-based portable ultrasound imaging system for point-of-care applications

We present a cost-effective portable ultrasound system based on a single field-programmable gate array (FPGA) for point-of-care applications. In the portable ultrasound system developed, all the ultrasound signal and image processing modules, including an effective 32-channel receive beamformer with pseudo-dynamic focusing, are embedded in an FPGA chip. For overall system control, a mobile processor running Linux at 667 MHz is used. The scan-converted ultrasound image data from the FPGA are directly transferred to the system controller via external direct memory access without a video processing unit. The potable ultrasound system developed can provide real-time B-mode imaging with a maximum frame rate of 30, and it has a battery life of approximately 1.5 h. These results indicate that the single FPGA-based portable ultrasound system developed is able to meet the processing requirements in medical ultrasound imaging while providing improved flexibility for adapting to emerging POC applications.     

基于洛伦兹锥规划的声矢量阵宽容自适应波束形成

针对矢量阵Capon波束形成对阵列误差尤其敏感这一不足,提出了运用洛伦兹锥规划(LCP,Lorentz Cone Pro.gramming)实现导向矢量范数约束来提高波束形成鲁棒性的方法.鉴于矢量水听器声压分量和振速分量对阵列误差敏感程度不同的特点,采用了"双线约束"的策略.将范数约束波束形成转化为LCP形式,通过内点...     

Bandwidth selective filter for the pre-excision of narrowband interference in broadband beamformers

A novel frequency domain excision filter for use in front of broadband adaptive beamformer systems is presented. The proposed frequency domain excision filter uses image processing techniques to determine the excision threshold such that only narrowband interference is removed from the received signal. By preexcising the received signal of narrowband interference the adaptive beamformer only has to remove partialband or broadband interferers. This frees up degrees of freedom (DoF) in the adaptive beamformer in mixed interference environments allowing for a greater interference suppression capability. The proposed preexcision system is simulated using a constrained space-time adaptive processor as well as a constrained suboptimal space-frequency adaptive processor. It is shown that when pre-excision is used in front of a beamformer the total number of interference sources that can be simultaneously rejected is increased as long as the beamformer's DoF are exceeded by narrowband interference.     

Aberrator integration error in adaptive imaging

Tissue speed of sound inhomogeneities cause significant degradation of medical ultrasound images. In some cases these inhomogeneities may be modeled as a thin time delay screen located at the face of the transducer. The effects of such near-field aberrations can be reduced by adding compensating time delays to the normal system focusing delays. Unfortunately array elements are generally large in at least one dimension when compared to variations in the aberrator, thus correction of the mean time delay on an element leaves residual variations in the time delay profile across that element. This paper presents theoretical expressions and simulation results describing the magnitude of this aberrator integration error. Simulations results are also presented which show the distortion of received pulses and degradation of point spread functions which results from aberrator integration error. These results indicate that aberrator integration error may be the dominant source of error in the implementation of adaptive imaging techniques and in phase aberration measurements. Thus, correction of near-field aberrations may be significantly more difficult than previously suspected     

The applicability of ultrasound dynamic receive beamformers to photoacoustic imaging

Ultrasound array transducers offer several advantages over mechanically-scanned transducers for photoacoustic imaging, including high imaging frame rates and dynamic focusing. Development of a photoacoustic array system can be accelerated by adapting existing commercial ultrasound systems and harnessing their performance-enhancing aspects such as parallel beamforming. One challenge faced when adapting commercial ultrasound systems for photoacoustic imaging is that the dynamic delay sequences required for focusing must account for one-way rather than two-way ultrasound wave propagation. Modifying the hardware may be difficult for developers and impossible for users, but some ultrasound systems provide a parameter, c: the speed of sound used to calculate these delays. A linear-array based ultrasound platform with parallel channel acquisition is used to compare experimental point-spread functions produced using an ultrasound beamformer with a scaled value of c to those produced by a photoacoustic beamformer. Scaling c by a factor of √2 provides the best image quality compared with adjustments by 1 and 2, but requires image rescaling, which can be done post-acquisition or by modification of the rendering software. Although optimal focusing is achieved for linear scanning, this is not the case for sector scanning, which requires angular and depth rescaling.