Vector Velocity Estimation Research Articles

Effects of beam steering angle and excitation frequency on blood flow imaging with plane wave imaging

The vector Doppler method was developed to overcome the limitations of conventional methods, which can only estimate axial velocities. Because the vector Doppler method uses steered beams, the excitation frequency is set lower than the resonance frequency of the transducer elements to prevent the generation of grating lobes. Although lowering the steering angle is another solution, a larger steering angle span leads to a more accurate estimation of velocity vectors. We have developed a method for estimating the steering angle from the received echo signals, which might enable an accurate estimation of velocity vectors even with small steering angles. In this study, the effects of steering angle and excitation frequency were investigated by numerical simulation and in vivo measurement of the carotid artery. The results showed that similar accuracies were obtained at high (6.94 MHz) and low (4.8 MHz) frequencies, and that better visualization of weak echoes from blood cells was achieved at 6.94 MHz.

Investigation on vector Doppler method for carotid artery wall with focused transmit beams produced from a cross-shaped probe

Conventional methods for estimating 1D or 2D velocities were developed for the dynamic measurement of carotid walls. However, a carotid wall moves in 3D due to a heart pulsation, and the wall motion velocity in the longitudinal-axis cross-section is affected by out-of-plane displacements that cannot be measured with a 1D array probe. To estimate the out-of-plane displacement, we proposed the cross-shaped probe. The cross-shaped probe can estimate 3D velocity vector with 256 transmit-receive channels. Single or multiple focused beams were transmitted by the main array of the cross-shaped probe, and the RF signals received all the elements were used for 3D velocity vector estimation based on the multi-angle Doppler method. Numerical simulations and basic experiments showed that out-of-plane displacements in the longitudinal-axis cross section can be estimated. Furthermore, the in vivo experiments on a human common carotid artery showed that arterial wall motion during a cardiac cycle can be measured.

Vehicle velocity estimation based on WSS/IMU with wheel slip recognition

Accurate velocity is of great significance to vehicle dynamic control, and vehicle velocity estimation based on wheel speed sensor (WSS) and inertial measurement unit (IMU) is more cost-effective than other sensors. Unavoidable wheel slip will result in velocity vector estimation error. To solve this problem, this paper proposed a novel wheel slip recognition criterion when using WSS/IMU for velocity estimation. The basic idea is to deduce the strict relationship between wheel speed, angular rate, and specific force when the wheel does not slip, and the slipping wheel will destroy this balance, which can be used to determine whether the wheel is slipping. Wheels identified as slipping are isolated from fusion, and only non-slipping wheels can be used for velocity estimation. In addition, the analysis shows that the wheel slip recognition is robust and works well even if there is an estimation error in the lateral velocity during vehicle turning. The co-simulation based on Carsim-Simulink shows that the proposed wheel slip recognition can ensure accurate vehicle velocity estimation at various working conditions. The real vehicle test further verified the important role of wheel slip recognition for velocity estimation.

Two-Dimensional Wavenumber Analysis Implemented in Ultrasonic Vector Doppler Method with Focused Transmit Beams

The multi-angle Doppler method was introduced for the estimation of velocity vectors by measuring axial velocities from multiple directions. We have recently reported that the autocorrelation-based velocity vector estimation could be ameliorated significantly by estimating the wavenumbers in two dimensions. Since two-dimensional wavenumber estimation requires a snapshot of an ultrasonic field, the method was first implemented in plane wave imaging. Although plane wave imaging is predominantly useful for examining blood flows at an extremely high temporal resolution, it was reported that the contrast in a B-mode image obtained with a few plane wave emissions was lower than that obtained with focused beams. In this study, the two-dimensional wavenumber analysis was first implemented in a framework with focused transmit beams. The simulations showed that the proposed method achieved an accuracy in velocity estimation comparable to that of the method with plane wave imaging. Furthermore, the performances of the methods implemented in focused beam and plane wave imaging were compared by measuring human common carotid arteries in vivo. Image contrasts were analyzed in normal and clutter-filtered B-mode images. The method with focused beam imaging achieved a better contrast in normal B-mode imaging, and similar velocity magnitudes and angles were obtained by both the methods with focused beam and plane wave imaging. In contrast, the method with plane wave imaging gave a better contrast in a clutter-filtered B-mode image and smaller variances in velocity magnitudes than those with focused beams.

Autonomous deck landing of a vertical take-off and landing unmanned aerial vehicle based on the tau theory

The research on autonomous landing of vertical take-off and landing (VTOL) unmanned aerial vehicles (UAVs) is well established. However, the research on autonomous deck landing using visual methods is relatively not so mature and many of them require the support of ground infrastructures. In order to reduce such dependencies, a ship landing guidance strategy based on on-board vision is studied. Considering the characteristics of the ship landing issue, we propose a three-phase landing scheme and a decision-making method to ensure landing safety is also studied. For improving the traditional two-dimensional (2D) optical-flow method, a three-dimensional (3D) velocity vector estimation method using image spherical optical flow is studied. Furthermore, a guidance law based on the tau theory is employed by only using the visual information of the line of sight to the target. In this phase, a trajectory-tracking controller is applied to generate the velocity commands of the UAV. Finally, the whole algorithm is validated by simulation in different wave conditions developed with Unity3D. Compared with traditional trajectory planning methods, our method does not require complex optimization iterations and can meet both the real-time and accuracy requirements of deck landing. The average tracking error of our method maintains in 0.2 m. Moreover, the whole algorithm runs efficiently at around 30 fps on a Raspberry-Pi 3B+ microcomputer which meets the real-time requirements.

Preliminary study on estimation of flow velocity vectors using focused transmit beams

High-frame-rate ultrasound imaging with plane wave transmissions is a predominant method of blood flow imaging, and methods for estimation of blood flow velocity vectors have been developed based on high-frame-rate imaging. On the other hand, in imaging of soft tissues, such as arterial walls and atherosclerotic plaques, high-frame-rate imaging sometimes suffers from high-level clutters. Even in observation of the arterial wall with a focused transmit beam, it would be highly beneficial if blood flow velocity vectors could be estimated simultaneously. We conducted a preliminary study on the estimation of blood flow velocity vectors based on a multi-angle Doppler method with focused transmit beam and parallel receive beamforming. It was shown that the lowest estimation error was achieved at a steering angle of 25° by simulation. Moreover, velocity vectors with typical velocity magnitudes and directions could be obtained by the proposed method in in vivo measurement of a carotid artery.

Velocity vector reconstruction for real-time phase-contrast MRI with radial Maxwell correction.

To develop an auto-calibrated image reconstruction for highly accelerated multi-directional phase-contrast (PC) MRI that compensates for (1) reconstruction instabilities occurring for phase differences near and (2) phase errors by concomitant magnetic fields that differ for individual radial spokes. A model-based image reconstruction for real-time PC MRI based on nonlinear inversion is extended to multi-directional flow by exploiting multiple flow-encodings for the estimation of velocity vectors. An initial smoothing constraint during iterative optimization is introduced to resolve the ambiguity of the solution space by penalizing phase wraps. Maxwell terms are considered as part of the signal model on a line-by-line basis to address phase errors by concomitant magnetic fields. The reconstruction methods are evaluated using simulated data and cross-sectional imaging of a rotating-disc, as well as in vivo for the aortic arch and cervical spinal canal at 3T. Real-time three-directional velocity mapping in the aortic arch is achieved at 1.8 × 1.8 × 6 mm3 spatial and 60 ms temporal resolution. Artificial phase wraps are avoided in all cases using the smoothness constraint. Inter-spoke differences of concomitant magnetic fields are effectively compensated for by the model-based image reconstruction with integrated radial Maxwell correction. Velocity vector reconstructions based on nonlinear inversion allow for high degrees of radial data undersampling paving the way for multi-directional PC MRI in real time. Whether a spoke-wise treatment of Maxwell terms is required or a computationally cheaper frame-wise approach depends on the individual application.

Improving image contrast and accuracy in velocity estimation by convolution filters for intracardiac blood flow imaging

In this study, the point spread function (PSF) of an ultrasound imaging system was estimated and used as a reference signal in a filtering method for improvement of image quality. The PSF of the imaging system was estimated from measured echo signals from an imaging target. Convolution filters (including deconvolution) were used for improvement of image contrast and spatial resolution. Furthermore, the accuracy in estimation of velocity vectors was evaluated for investigation of the impact of the proposed filters on velocity estimation. In the phantom experiment, contrast of the B-mode image was improved from 76.4 dB to 81.1 dB and 77.8 dB using the convolution and deconvolution filters, respectively. Also, the two-dimensional (2D) velocity distribution in the phantom was estimated by the block matching method, and the bias error (BE) in the estimated lateral velocity was reduced from −19.7% to 2.16% and 2.29% using the convolution and the deconvolution filters, respectively.

Tapered Vector Doppler for Improved Quantification of Low Velocity Blood Flow.

A new vector velocity estimation scheme is developed, termed tapered vector Doppler (TVD), aiming to improve the accuracy of low velocity flow estimation. This is done by assessing the effects of singular value decomposition (SVD) and finite impulse response (FIR) filters and designing an estimator which accounts for signal loss due to filtering. Synthetic data created using a combination of in vivo recordings and flow simulations were used to investigate scenarios with low blood flow, in combination with true clutter motion. Using this approach, the accuracy and precision of TVD was investigated for a range of clutter-to-blood and signal-to-noise ratios. The results indicated that for the investigated carotid application and setup, the SVD filter performed as a frequency-based filter. For both SVD and FIR filters, suppression of the clutter signal resulted in large bias and variance in the estimated blood velocity magnitude and direction close to the vessel walls. Application of the proposed tapering technique yielded significant improvement in the accuracy and precision of near-wall vector velocity measurements, compared to non-TVD and weighted least squares approaches. In synthetic data, for a blood SNR of 5 dB, and in a near-wall region where the average blood velocity was 9 cm/s, the use of tapering reduced the average velocity magnitude bias from 26.3 to 1.4 cm/s. Complex flow in a carotid bifurcation was used to demonstrate the in vivo performance of TVD, and it was shown that tapering enables vector velocity estimation less affected by clutter and clutter filtering than what could be obtained by adaptive filter design only.

1Pa5-3 Investigation on estimation of velocity vectors for blood flow measurements

1Pa5-3 Investigation on estimation of velocity vectors for blood flow measurements

Vessel Velocity Estimation and Tracking From Doppler Echoes of T/R-R Composite Compact HFSWR

Vessel speed and heading are two important kinematic parameters describing its state of motion. However, due to low spatial resolution of a compact high-frequency surface wave radar (HFSWR), vessel speed and heading cannot always be accurately estimated. Since HFSWR can measure vessel Doppler velocity with relatively high accuracy, it is possible to estimate a vessel's vector velocity based on two Doppler velocities measured along two different directions. In this article, a newly developed T/R-R composite compact HFSWR system is introduced, and a corresponding vessel velocity estimation method which employs a target's radial velocity and elliptical velocity, respectively, measured by the monostatic (T/R) and bistatic (T-R) settings is proposed. First, monostatic and bistatic tracks are independently generated using a multitarget tracking algorithm. Then, the obtained monostatic and bistatic tracks are matched using a track-to-track association method to determine the track pair belonging to each target. Subsequently, the associated track pairs are combined to produce fused tracks for improving positioning accuracy. Finally, vessel vector velocity is estimated based on the radial and elliptical velocities as well as the fused target position. Comparisons of vector velocity estimation results from radar field data with corresponding automatic identification system data demonstrate that the average root-mean-square-errors of the estimated speed and heading are 0.48 km/h and 3.9 $^{\circ }$ , respectively, which meets the practical requirements of a maritime surveillance system. Moreover, the velocity estimation error is analyzed via theoretical derivation and experimental verification. The proposed method shows good potential in further improving the tracking accuracy.

An Elaborated Signal Model for Simultaneous Range and Vector Velocity Estimation in FMCW Radar.

A rigorous mathematical description of the signal reflected from a moving object for radar monitoring tasks using linear frequency modulated continuous wave (LFMCW) microwave radars is proposed. The mathematical model is based on the quasi-relativistic vector transformation of coordinates and Lorentz time. The spatio-temporal structure of the echo signal was obtained taking into account the transverse component of the radar target speed, which made it possible to expand the boundaries of the range of measuring the range and speed of vehicles using LFMCW radars. An algorithm for the simultaneous estimation of the range, radial and transverse components of the velocity vector of an object from the observation data of the time series during one frame of the probing signal is proposed. For an automobile 77 GHz microwave LFMCW radar, a computer experiment was carried out to measure the range and velocity vector of a radar target using the developed mathematical model of the echo signal and an algorithm for estimating the motion parameters. The boundaries of the range for measuring the range and speed of the target are determined. The results of the performed computer experiment are in good agreement with the results of theoretical analysis.

An Approximate ML Estimator for Moving Target Localization in Distributed MIMO Radars

This letter deals with the problem of moving target localization in distributed multiple-input multiple-output (MIMO) radar systems using time delay (TD) and Doppler shift (DS) measurements. The proposed solution to this problem consists of two stages. In the first stage, an initial estimation of target location is obtained by solving the formulated maximum likelihood (ML) problem based on the TD measurements. In the second stage, by recognizing the obtained position estimate in the previous stage as a priori data and exploiting the DS measurements, another ML problem is formulated, which is efficiently solved via a tractable numerical method to produce a simultaneous estimation of target position and velocity vectors. Overall, the proposed method significantly outperforms the state-of-the-art algorithms under Gaussian noise model as corroborated by numerical simulations.

Low-Order Velocity Estimation and Acoustic Noise Generation by a Turbulent Wall Jet

A method for estimating the velocity fluctuations, hydrodynamic pressure fluctuations, and far-field acoustic pressure in a planar turbulent wall jet is examined. The Reynolds number based on nozzle height and exit velocity is 25,500. Streamwise-aligned, two-component particle image velocimetry and surface pressure measurements are obtained synchronously along the center line of the wall jet. Modified stochastic estimation is used to estimate a low-dimensional representation of the time-dependent velocity field, and performance metrics for the evaluation of the estimates are presented. The use of proper orthogonal decomposition in the estimation is evaluated against the estimation of individual velocity vectors from the measurements to investigate the filtering effect of using a subset of proper orthogonal decomposition modes in the velocity reconstruction. The velocity estimates are used to solve Poisson’s equation for the time-dependent hydrodynamic pressure fluctuations. Curle’s acoustic analogy is evaluated using the estimated velocity and pressure and compared with far-field acoustic measurements via a phased array of microphones. The estimated acoustic spectrum scaled by spanwise integration width is comparable to scaled measurements of the acoustic spectrum. The estimation method highlights the importance of the interaction between the pressure and velocity fields to the acoustic generation process.

4-D Intracardiac Ultrasound Vector Flow Imaging-Feasibility and Comparison to Phase-Contrast MRI.

In vivo characterization of intracardiac blood velocity vector fields may provide new clinical information but is currently not available for bedside evaluation. In this paper, 4-D vector flow imaging for intracardiac flow assessment is demonstrated using a clinical ultrasound (US) system and a matrix array transducer, without the use of contrast agent. Two acquisition schemes were developed, one for full volumetric coverage of the left ventricle (LA) at 50 vps and a 3-D thick-slice setup with continuous frame acquisition (4000 vps), both utilizing ECG-gating. The 3-D vector velocity estimates were obtained using a novel method combining phase and envelope information. In vitro validation in a rotating tissue-mimicking phantom revealed velocity estimates in compliance with the ground truth, with a linear regression slope of 0.80, 0.77, and 1.03 for the , , and velocity components, and with standard deviations of 2.53, 3.19, and 0.95 cm/s, respectively. In vivo measurements in a healthy LV showed good agreement with PC-MRI. Quantitative analysis of energy loss (EL) and kinetic energy (KE) further showed similar trends, with peak KE at 1.5 and 2.4 mJ during systole and 3.6 and 3.1 mJ for diastole for US and PC-MRI. Similar for EL, 0.15- 0.2 and 0.7 mW was found during systole and 0.6 and 0.7 mW during diastole, for US and PC-MRI, respectively. Overall, a potential for US as a future modality for 4D cardiac vector flow imaging was demonstrated, which will be further evaluated in clinical studies.

First Spaceborne SAR-GMTI Experimental Results for the Chinese Gaofen-3 Dual-Channel SAR Sensor.

In spaceborne synthetic aperture radar (SAR) sensors, it is a challenging task to detect ground slow-moving targets against strong clutter background with limited spatial channels and restricted pulse repetition frequency (PRF). In this paper, we evaluate the image-based dual-channel SAR-ground moving target indication (SAR-GMTI) workflow for the Gaofen-3 SAR sensor and analyze the impact of strong azimuth ambiguities on GMTI when the displaced phase center antenna (DPCA) condition is not fully satisfied, which has not been demonstrated yet. An effective sliding window design technique based on system parameters analysis is proposed to deal with azimuth ambiguities and reduce false alarm. In the SAR-GMTI experiments, co-registration, clutter suppression, constant false alarm rate (CFAR) detector, vector velocity estimation and moving target relocation are analyzed and discussed thoroughly. With the real measured data of the Gaofen-3 dual-channel SAR sensor, the GMTI capability of this sensor is demonstrated and the effectiveness of the proposed method is verified.

Directional Transverse Oscillation Vector Flow Estimation.

A method for estimating vector velocities using transverse oscillation (TO) combined with directional beamforming is presented. In directional TO (DTO), a normal focused field is emitted and the received signals are beamformed in the lateral direction transverse to the ultrasound beam to increase the amount of data for vector velocity estimation. The approach is self-calibrating as the lateral oscillation period is estimated from the directional signal through a Fourier transform to yield quantitative velocity results over a large range of depths. The approach was extensively simulated using Field IIpro and implemented on the experimental Synthetic Aperture Real-time Ultrasound System (SARUS) scanner in connection with a BK Medical 8820e convex array transducer. Velocity estimates for DTO are found for beam-to-flow angles of 60°, 75°, and 90°, and vessel depths from 24 to 156 mm. Using 16 emissions, the standard deviation (SD) for angle estimation at depths ranging from 24 to 104 mm is between 6.01° and 0.93° with a mean SD of 2.8°. The mean relative SD for the lateral velocity component is 9.2% and the mean relative bias -3.4% or four times lower than for traditional TO. The approach also works for deeper lying vessels with a slight increase in SD to 15.7%, but a maintained bias of -3.5% from 126 to 156 mm. Data for a pulsating flow have also been acquired for 15 cardiac cycles using a CompuFlow 1000 pump. The relative SD was here 7.4% for a femoral artery waveform.

Vector velocity estimation of blood flow - A new application in medical ultrasound.

Vector flow techniques in the field of ultrasound encompass different pulse emission and estimation strategies. Numerous techniques have been introduced over the years, and recently commercial implementations usable in the clinic have been made. A number of clinical papers using different vector velocity approaches have been published. This review will give an overview of the most significant in vivo results achieved with ultrasound vector flow techniques, and will outline some of the possible clinical applications for vector velocity estimation in the future.

Estimation of velocities using GNSS observations in the GNSS Data Analysis Center of GAO NASU for further geodynamical studies

Global satellite navigation systems (GNSS) has firmly entered not only in the daily life of society, but also widely used in various fields of scientific application. The possibility of conducting continuous observations at permanent GNSS stations, which do not depend on weather conditions, allowed to accumulate long periods of observations. All this led to the acquisition of precision time coordinate with accuracy of several millimeters. One of the first steps in the study of the local level of the crustal deformation is the estimation of the values of the displacement velocities of the GNSS stations. One of the simplest and most widespread ways of representing the horizontal movements of the earth's surface occurring within the region under study is the acquisition of a velocity field. GNSS data analysis center of GAO NASU received estimates of velocity vectors for 233 GNSS stations (in coordinate system IGb08), 202 of which are located in Ukraine. The maximum assessment period was from December 7, 1997 – January 28, 2017, or 6,993 days (approximately 20 years). The rate estimation is based on GNSS observations of state, academic, university and commercial networks of Ukraine. The velocity vectors were obtained using the Bernese GNSS Software Ver. 5.2 (ADDNEQ2 and FODITS software modules were used) recommended by the GNSS Data Analysis Centers, in particular by the EUREF European Center for research of this type. The obtained estimates of the velocity vectors fully coincide with the movement of the Eurasian lithospheric plate. For further use in studies on the deformation of the Earth's crust, each GNSS station should be thoroughly tested for possible effects (caused by the operation of the apparatus, human factor, etc.), as well as to satisfy the minimum observation period of three years.

An Extended Least Squares Method for Aliasing-Resistant Vector Velocity Estimation.

An extended least squares method for robust, angle-independent 2-D vector velocity estimation using plane-wave ultrasound imaging is presented. The method utilizes a combination of least squares regression of Doppler autocorrelation estimates and block matching to obtain aliasing-resistant vector velocity estimates. It is shown that the aliasing resistance of the technique may be predicted using a single parameter, which is dependent on the selected transmit and receive steering angles. This parameter can therefore be used to design the aliasing-resistant transmit-receive setups. Furthermore, it is demonstrated that careful design of the transmit-receive steering pattern is more effective than increasing the number of Doppler measurements to obtain robust vector velocity estimates, especially in the presence of higher order aliasing. The accuracy and robustness of the method are investigated using the realistic simulations of blood flow in the carotid artery bifurcation, with velocities up to five times the Nyquist limit. Normalized root-mean-square (rms) errors are used to assess the performance of the technique. At -5 dB channel data blood SNR, rms errors in the vertical and horizontal velocity components were approximately 5% and 15% of the maximum absolute velocity, respectively. Finally, the in vivo feasibility of the technique is shown by imaging the carotid arteries of healthy volunteers.