Broadband minimum variance beamforming for ultrasound imaging

A minimum variance (MV) approach for nearfield beamforming of broadband data is proposed. The approach is implemented in the frequency domain, and it provides a set of adapted, complex apodization weights for each frequency subband. The performance of the proposed MV beamformer is tested on simulated data obtained using Field II. The method is validated using synthetic aperture data and data obtained from a plane wave emission. Data for 13 point targets and a circular cyst with a radius of 5 mm are simulated. The performance of the MV beamformer is compared with delay-and-sum (DS) using boxcar weights and Hanning weights and is quantified by the full width at half maximum (FWHM) and the peak-side-lobe level (PSL). Single emission {DS boxcar, DS Hanning, MV} provide a PSL of {-16, -36, -49} dB and a FWHM of {0.79, 1.33, 0.08} mm. Using all 128 emissions, {DS boxcar, DS Hanning, MV} provides a PSL of {-32, -49, -65} dB, and a FWHM of {0.63, 0.97, 0.08} mm. The contrast of the beamformed single emission responses of the circular cyst was calculated as {-18, -37, -40} dB. The simulations have shown that the frequency subband MV beamformer provides a significant increase in lateral resolution compared with DS, even when using considerably fewer emissions. An increase in resolution is seen when using only one single emission. Furthermore, the effect of steering vector errors is investigated. The steering vector errors are investigated by applying an error of the sound speed estimate to the ultrasound data. As the error increases, it is seen that the MV beamformer is not as robust compared with the DS beamformer with boxcar and Hanning weights. Nevertheless, it is noted that the DS does not outperform the MV beamformer. For errors of 2% and 4% of the correct value, the FWHM are {0.81, 1.25, 0.34} mm and {0.89, 1.44, 0.46} mm, respectively.     

Minimum variance beamforming applied to ultrasound imaging with a partially shaded aperture

Shadowing of an imaging aperture occurs when ultrasound beams are partially obstructed by an acoustically hard tissue, e.g., bone tissue. This effect leads to reduced resolution and, in some cases, geometrical distortion. In this paper, we initially introduce a binary apodization model to simulate effects of the shadowing on the point scatterers located close to a bone structure. Further, in a simulation study and an in vitro experiment, the minimum variance (MV) beamforming method is employed to image scatterers partly located in the shadow of bone. We show that the MV beamformer can result in a distorted image when the imaging aperture is highly obstructed by the bone structure. This distortion can be seen as an apparent lateral shift of the point spread function and a decrease in the sensitivity. Based on the signal power across the aperture, we adaptively determine the shadowed elements and discard their corresponding data from the covariance matrix to improve the MV beamformer performance. This modified MV beamformer can retain the resolution and compensate for the apparent lateral shifting and signal attenuation for the shadowed point scatterers.     

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.     

Compounded direct pixel beamforming for medical ultrasound imaging

In this paper, a new compounded direct pixel beamforming (CDPB) method is presented to remove blurring artifacts introduced by ultrasound scan conversion. In CDPB, receive focusing is directly performed on each display pixel in Cartesian coordinates using the raw RF data from adjacent transmit firings so that artifacts from the scan conversion can be removed. In addition, the energy variations resulting from the distance between the transmit scanline and display pixel are compensated by utilizing the gain factor obtained from the ultrasound beam pattern. The proposed CDPB method was evaluated using simulation and in vivo liver data acquired by a commercial ultrasound machine equipped with a research package. The experimental results showed that the proposed CDPB method improved the information entropy contrast (IEC) by 23.6% compared with the conventional scan conversion method and it reduced the blocking artifacts factor (BAF) by 16.4% over the direct pixel-based focusing method. These results indicate the proposed new direct pixel beamforming method could be used to enhance image quality in medical ultrasound imaging.     

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.     

Beamspace adaptive beamforming for ultrasound imaging

Applying the Capon adaptive beamformer in medical ultrasound imaging results in enhanced resolution by improving the interference-suppressing capabilities of the array. This improvement comes at the expense of an increased computational complexity. We have investigated the application of a beamspace adaptive beamformer for medical ultrasound imaging, which can be used to achieve reduced computational complexity with performance comparable to that of the Capon beamformer. The idea behind beamspace beamforming is that, instead of using the spatial statistics of the elements in the array to differentiate between signals and interference, we use the spatial statistics of a set of orthogonal beams, which are formed in different directions. This represents a shift from element space to beamspace. Because the majority of interference in medical ultrasound imaging is constrained to a limited spatial interval due to the focused transmit beam, this latter space can be reduced to a dimension that is lower than that of element space. We show, using simulations and experimental data, that this dimension can be selected as low as 3 while still achieving performance comparable to its element space counterpart.     

Application of a beamforming technique to ultrasound imaging innondestructive testing

Many innovations in the modern testing of materials make use of ultrasound. As a result, ultrasound has become extremely important to nondestructive testing of complete engineered systems. However, despite the fact that ultrasound inspection techniques are based on well-established principles, a few key problems pertaining to their application still remain unresolved. One of these problems deals with materials having complex geometries, often making the scanning/data collection processes time consuming. Consequently, fast and accurate mechanisms for testing components with awkward configurations have been the focus of attention in modern nondestructive testing research. In this paper, the data independent beamformer is studied as a potential method to reduce ultrasonic data acquisition time. The finite element method (FEM) is used as a testbed to mimic the ultrasound measurements by simulating the action of a transducer array. Tests reveal that when the weights of the interpolating filters (beamformers) are adjusted properly, they can indeed be used to predict A-scan signals from a data set produced by a transducer moving in a line-scan direction at nonuniform increments; hence, reducing the data acquisition time. The same filter weights also predict accurately A-scan signals from another data set produced by the same transducer moving at nonuniform increments for a different material geometry     

Optimum beamforming for sidelobe reduction in ultrasound imaging

A constrained adaptive beamforming in a deterministic sense is considered for side lobe reduction, leading to an adaptive weighting of the uniform delay-and-sum beamformer; based upon this, the coherence factor and other similar methods are interpreted as beamforming methods. A generalized form of the weighting factor for the side lobe reduction is also established. It is shown through simulations that restricting the apodization vector to a parametric representation through a discrete Fourier transform or discrete cosine transform can result in higher quality images with fewer artifacts and enhanced contrast properties compared with images obtained through the coherence factor-like methods.     

Real-time 3-D ultrasound imaging using sparse synthetic aperture beamforming

A method for real-time three-dimensional (3-D) ultrasound imaging using a mechanically scanned linear phased array is proposed. The high frame rate necessary for real-time volumetric imaging is achieved using a sparse synthetic aperture beamforming technique utilizing only a few transmit pulses for each image. Grating lobes in the two-way radiation pattern are avoided by adjusting the transmit element spacing and the receive aperture functions to account for the missing transmit elements. The signal loss associated with fewer transmit pulses is minimized by increasing the power delivered to each transmit element and by using multiple transmit elements for each transmit pulse. By mechanically rocking the array, in a way similar to what is done with an annular array, a 3-D set of images can be collected in the time normally required for a single image.     

Iterative bit and power allocation for multi-cell orthogonal frequency division multiplexing with minimum variance distortionless response beamforming

This paper develops bit and power allocation schemes with beamforming for multi-cell orthogonal frequency division multiplexing (OFDM) systems on uplink. The model of the multi-cell channel with frequency reuse is considered. The transmit signal from each mobile causes interference to the received signals of other base stations. The schemes aim to minimise the total mobile transmit power while satisfying the required data rate and the bit error rate (BER) of each mobile. The proposed schemes offer better performance than that of the fixed bit allocation method. The proposed distributed allocation scheme reduces computational complexity compared to the proposed centralised multi-user greedy method with insignificant performance degradation. The simulation results are presented to demonstrate the efficacy of the proposed schemes.     

Minimum variance ultrasonic imaging applied to an in situ sparse guided wave array

Ultrasonic guided wave imaging with a sparse, or spatially distributed, array can detect and localize damage over large areas. Conventional delay-and-sum images from such an array typically have a relatively high noise floor, however, and contain artifacts that often cannot be discriminated from damage. Considered here is minimum variance distortionless response (MVDR) imaging, which is a variation of delay-and-sum imaging whereby weighting coefficients are adaptively computed at each pixel location. Utilization of MVDR significantly improves image quality compared with delay-and-sum imaging, and additional improvements are obtained from incorporation of a priori scattering information in the MVDR method, use of phase information, and instantaneous windowing. Simulated data from a through-hole scatterer are used to illustrate performance improvements, and a performance metric is proposed that allows for quantitative comparisons of images from a known scatterer. Experimental results from a through-hole scatterer are also provided that illustrate imaging efficacy.     

Direct sampled I/Q beamforming for compact and very low-cost ultrasound imaging

A wide variety of beamforming approaches are applied in modern ultrasound scanners, ranging from optimal time domain beamforming strategies at one end to rudimentary narrowband schemes at the other. Although significant research has been devoted to improving image quality, usually at the expense of beamformer complexity, we are interested in investigating strategies that sacrifice some image quality in exchange for reduced cost and ease in implementation. This paper describes the direct sampled in-phase/quadrature (DSIQ) beamformer, which is one such low-cost, extremely simple, and compact approach. DSIQ beamforming relies on phase rotation of I/Q data to implement focusing. The I/Q data are generated by directly sampling the received radio frequency (RF) signal, rather than through conventional demodulation. We describe an efficient hardware implementation of the beamformer, which results in significant reductions in beamformer size and cost. We present the results of simulations and experiments that compare the DSIQ beamformer to more conventional approaches, namely, time delay beamforming and traditional complex demodulated I/Q beamforming. Results that show the effect of an error in the direct sampling process, as well as dependence on signal bandwidth and system f number (f#) are also presented. These results indicate that the image quality and robustness of the DSIQ beamformer are adequate for low end scanners. We also describe implementation of the DSIQ beamformer in an inexpensive hand-held ultrasound system being developed in our laboratory.     

Contrast response analysis for medical ultrasound imaging

Traditional measures of spatial resolution are helpful but incomplete for characterizing the imaging performance of medical ultrasound systems because the challenge is not so much resolving strong point reflectors as limiting the impact of stronger scattering regions on weaker regions. This paper discusses the use of an alternative measure which is based on the ability of a system to accurately image an anechoic region surrounded by a uniform scattering medium. This measure, called contrast response, includes effects of both mainlobe width and sidelobe level. Since the impulse response of a linear system to a target is the convolution of the system spatial impulse response (beam pattern) and the target scattering function, the system output can be described by a three dimensional integral. The contrast response is defined as the ratio of this system output when the anechoic target is not present to the output when it is present, evaluated over a range of target sizes. Contrast response analysis is useful for both system design and performance comparison. Examples are presented which compare the performance of systems with different apodization functions and aperture sizes. This analysis approach suggests why the strong window functions popular in signal processing have not been used for apodization in medical ultrasound and why 256 channel systems have not demonstrated a dramatic performance improvement over 128 channel systems     

Fresnel-based beamforming for low-cost portable ultrasound

In this paper, we propose a modified electronic Fresnel-based beamforming method for low-cost portable ultrasound systems. This method uses a unique combination of analog and digital beamforming methods. Two versions of Fresnel beamforming are presented in this paper: 4-phase (4 different time delays or phase shifts) and 8-phase (8 different time delays or phase shifts). The advantage of this method is that a system with 4 to 8 transmit channels and 2 receive channels with a network of switches can be used to focus an array with 64 to 128 elements. The simulation and experimental results show that Fresnel beamforming image quality is comparable to traditional delay-and-sum (DAS) beamforming in terms of spatial resolution and contrast-to-noise ratio (CNR) under certain system parameters. With an f-number of 2 and 50% signal bandwidth, the experimental lateral beamwidths are 0.54, 0.67, and 0.66 mm and the axial pulse lengths are 0.50, 0.51, and 0.50 mm for DAS, 8-phase, and 4-phase Fresnel beamforming, respectively. The experimental CNRs are 4.66, 4.42, and 3.98, respectively. These experimental results are in good agreement with simulation results.     

In-vivo synthetic aperture flow imaging in medical ultrasound

A new method for acquiring flow images using synthetic aperture techniques in medical ultrasound is presented. The new approach makes it possible to have a continuous acquisition of flow data throughout the whole image simultaneously, and this can significantly improve blood velocity estimation. Any type of filter can be used for discrimination between tissue and blood flow without initialization, and the number of lines used for velocity estimation is limited only by the nonstationarity of the flow. The new approach is investigated through both simulations and measurements. A flow rig is used for generating a parabolic laminar flow, and a research scanner is used for acquiring RF data from individual transducer elements. A reference profile is calculated from a mass flow meter. The parabolic velocity profile is estimated using the new approach with a relative standard deviation of 2.2% and a mean relative bias of 3.4% using 24 pulse emissions at a flow angle of 45 degrees. The 24 emissions can be used for making a full-color flow map image. An in-vivo image of flow in the carotid artery for a 29-year-old male also is presented. The full image is acquired using 24 emissions.     

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.     

The progressive focusing correction technique for ultrasound beamforming

This work presents a novel method for digital ultrasound beamforming based on programmable table look-ups, in which vectors containing coded focusing information are efficiently stored, achieving an information density of a fraction of bit per acquired sample. Timing errors at the foci are within half the period of a master clock of arbitrarily high frequency to improve imaging quality with low resource requirements. The technique is applicable with conventional as well as with deltasigma converters. The bit-width of the focusing code and the number of samples per focus can be defined to improve both memory size and F# with controlled timing errors. In the static mode, the number of samples per focus is fixed, and in the dynamic approach that figure grows progressively, taking advantage of the increasing depth of focus. Furthermore, the latter has the lowest memory requirements. The technique is well suited for research purposes as well as for real-world applications, offering a degree of freedom not available with other approaches. It allows, for example, modifying the sampling instants to phase aberration correction, beamforming in layered structures, etc. The described modular and scalable prototype has been built using low-cost field programmable gate arrays (FPGAs). Experimental measurements are in good agreement with the theoretically expected errors.     

A cautious minimum variance controller with ARIMA disturbances

This article investigates a Cautious Minimum Variance (CMV) control approach for controlling industrial process variability when the model parameters are estimated from data and subject to uncertainty. CMV control has a number of advantages over traditional robust control methods. It incorporates probabilistic, as opposed to deterministic, measures of parameter uncertainty, which are more consistent with the statistical methods typically used to estimate industrial process models. CMV control is also more consistent with the objective of minimizing process variability, since parameter uncertainty is treated simply as an additional source of variation. CMV results have previously been derived for the case where the process disturbance follows a first-order integrated moving average model. This work extends the results to autoregressive moving average and autoregressive integrated moving average disturbances.