Vector Velocity Estimation Research Articles

Estimating the blood velocity vector using aperture domain data

Most conventional blood flow estimation methods measure only the axial component of the blood velocity vector. In this study, we developed a new method for two-dimensional (2-D) velocity vector estimation in which time shifts resulting from blood motion are calculated for the individual channels using aperture domain data. This allows the construction of a time-shift profile along the array direction as a function of channel index, which is approximated by a first-order polynomial whose zeroth-order and first-order terms can be used to determine the axial and lateral velocity components, respectively. The efficacy of the proposed method was verified by simulations and experiments in which the transducer array had 64 elements, an aperture size of 1.96 cm, and a center frequency of 5 MHz. The flow velocity ranged from 5 to 35 cm/s and the Doppler angle ranged from 0 degrees to 90 degrees. The experimental results show that the accuracy of axial velocity estimation is higher for the new method than for the autocorrelation-based conventional method when the signal-to-noise ratio is larger than 0 dB. The mean estimation error for the axial velocity component is 2.18% for the new method, compared to 4.51% for the conventional method. The mean estimation error for the lateral velocity component is 15%, which is comparable to existing methods.

Estimation of Velocity Vectors in Synthetic Aperture Ultrasound Imaging

A method for determining both velocity magnitude and angle in a synthetic aperture ultrasound system is described. The approach uses directional beamforming along the flow direction and cross correlation to determine velocity magnitude. The angle of the flow is determined from the maximum normalized correlation calculated as a function of angle. This assumes the flow direction is within the imaging plane. Simulations of the angle estimation method show both biases and standard deviations of the flow angle estimates below 3 degrees for flow angles from 20 degrees to 90 degrees (transverse flow). The method is also investigated using data measured by an experimental ultrasound scanner from a flow rig. A commercial 128 element 7-MHz linear array transducer is used, and data are measured for flow angles of 60 degrees and 90 degrees . Data are acquired using the RASMUS experimental ultrasound scanner, which samples 64 channels simultaneously. A 20-micros chirp was used during emission and eight virtual transmit sources were created behind the transducer using 11 transmitting elements. Data from the eight transmissions are beamformed and coherently summed to create high-resolution lines at different angles for a set of points within the region of flow. The velocity magnitude is determined with a precision of 0.36% (60 degrees) and 1.2% (90 degrees), respectively. The 60 degrees angle is estimated with a bias of 0.54 degrees and a standard deviation of 2.1 degrees. For 90 degrees the bias is 0.0003 degrees and standard deviation 1.32 degrees. A parameter study with regard to correlation length and number of emissions is performed to reveal the accuracy of the method. Real time data covering 2.2 s of the carotid artery of a healthy 30-year-old male volunteer is acquired and then processed offline using a computer cluster. The direction of flow is estimated using the above mentioned method. It is compared to the flow angle of 106 degrees with respect to the axial direction, determined visually from the B-mode image. For a point in the center of the common carotid artery, 76% of the flow angle estimates over the 2.2 s were within 10 degrees of the visually determined flow angle. The standard deviation of these estimates was below 2.7 degrees. Full color flow maps from different parts of the cardiac cycle are presented, including vector arrows indicating both estimated flow direction and velocity magnitude.

Vector-velocity estimation in swept-scan using a K-space approach

The swept-scan technique (i.e., continuously moving a single-crystal transducer during pulse-echo data acquisition) is used in high-frequency, ultrasonic flow imaging. Relative to the conventional step-scan technique, swept scanning improves the rate of data acquisition and enables near-real-time, high-frequency color flow mapping. However, the continuous transducer movement may have non-negligible effects on accuracy of velocity estimation. This paper introduces a spatial frequency domain (i.e., k-space) approach that quantifies the effects of both lateral and axial motions in a swept scan. It is shown that the k-space representation is equivalent to a Doppler-radio frequency (RF) frequency domain representation, and that transducer movement in the swept-scan technique results in a change in Doppler bandwidth. In addition, a vector velocity estimator is developed based on the proposed k-space approach. Both simulations and flow-phantom experiments were performed to evaluate the performance of the proposed vector velocity estimator. A 45-MHz transducer was scanned at 20 mm/s. The Doppler angle ranged from 29 degrees to 90 degrees, and the flow velocities ranged from 15 to 30 mm/s. The results show that the proposed k-space vector velocity estimator exhibited a mean error of 2.6 degrees for flow-direction estimation, with the standard deviation ranging from 2.2 degrees to 8.2 degrees. In comparison, for the conventional spectral-broadening-based vector velocity estimator ignoring the swept-scan effect, the mean error became 15 degrees and the standard deviations were from 2.7 degrees to 6.6 degrees.

Sea surface velocity vector retrieval using dual-beam interferometry: first demonstration

The dual-beam interferometer consists of two interferometric synthetic aperture radars (InSARs), one squinted at 20/spl deg/ forward of broadside, and the other 20/spl deg/ aft, to allow measurement of vector surface velocity with only a single aircraft pass. Estimates of surface velocity vectors in the coastal region during high tidal flow are presented. The data were gathered over the barrier islands west of Fort Myers, Florida, as part of a March 2004 deployment. Whereas no detailed bathymetry data were available, high-quality aerial photography appears to be a useful tool in inferring bottom topography and possible current obstructions. The retrieved velocity field clearly follows the expected outflow pattern. While comparisons with tidal current magnitudes predicted by the U.S. National Ocean Service do reveal discrepancies of up to 0.5 m/s, these differences are most likely due to the contribution of ocean surface waves to the overall InSAR velocity measurement. Velocity retrievals for the same area based on the data from different tracks show good consistency. The results constitute the first demonstration of vector retrieval of the surface velocity field with a single-pass InSAR system and confirm the robustness of the dual-beam interferometry principle.

Techniques of Wind Vector Estimation from Data Measured with a Scanning Coherent Doppler Lidar

Abstract The results of a theoretical study of the feasibility of wind velocity vector estimation from data, measured with a scanning coherent Doppler lidar, are presented. The estimation techniques considered are (a) the direct sine wave fitting (DSWF) and the filtered sine wave fitting (FSWF), where at first the radial wind velocities are estimated and then the wind vector is estimated from the dependence of the radial velocity versus the azimuth angle of the scanning; and (b) the maximum of the function of accumulated spectra (MFAS) and the maximum likelihood for the wind vector estimation (WV ML), where the wind vector is estimated directly from data measured by a scanning lidar without intermediate estimation of the radial wind velocities. It has been shown that due to strong averaging of noise fluctuations in accumulated spectra, the WV ML and MFAS techniques allow one to estimate the wind vector with acceptable accuracy at an essentially lower signal-to-noise ratio (SNR) than the methods of the sin...

A procedure for three-dimensional angular velocity determination using a star sensor in high-rate rotation modes

This paper presents an application for modern star trackers aimed at the estimation of the spacecraft angular velocity vector on the basis of the star field images acquired during fast rotations, when star identification and tracking are not possible. Angular rates in the range 2–8°/s are considered, which strongly affect the characteristics of the acquirable images, in particular for shape and brightness. The procedure consists in the exploitation of the rigid motion equations to identify the rotation that best fits the observed star trajectories in the sensor field of view. Its coverage capability is analysed with reference to the sensitivity of state-of-the-art photodetectors. The probability of an adequate acquisition is shown to be 0.80 with random pointing and rotation axis over the celestial sphere. Firstly, the accuracy of the procedure is discussed in numerical tests. Then, end-to-end tests are reported, which have been operated by implementing the procedure in a hardware sensor model that acquires simulated star field scenes in a laboratory facility. Both the validations point out that the accuracy of 1°/s, suggested by the European Space Agency for this kind of application, has been achieved. Moreover, the rate of rotation about axes perpendicular to the boresight can be computed with accuracy one order of magnitude better.

Poleward‐moving HF radar flow bursts in the cusp: Transient changes in flow speed or direction?

Poleward‐moving line‐of‐sight velocity “flow bursts” have been observed in the cusp by two southern hemisphere SuperDARN HF radars with overlapping fields‐of‐view. This has allowed the estimation of unambiguous two‐dimensional velocity vectors in the vicinity of the “flow bursts”. Rather than showing enhancements in the flow magnitude, the velocity vectors suggest that the line‐of‐sight velocity enhancements are a result of a change in the direction of the flow associated with latitudinal motion of the convection reversal boundary. These observations may have important implications for understanding the ionospheric footprint of flux transfer events, and also illustrate that caution is needed when interpreting line‐of‐sight velocity data from single radars.

Limited diffraction beams and their applications on signal processing

Limited diffraction beams such as Bessel beams and X waves have been studied recently. These beams have many potential applications in medical imaging, tissue identification, blood flow velocity vector estimation, nondestructive evaluation of industrial materials, optical communications, and other physics related areas such as electromagnetics and optics. In this talk, fundamentals of limited diffraction beams will be presented. Results of applications of X wave theory on high-frame rate medical imaging will be shown. Applications of these beams in other areas, especially, in signal processing will be discussed. [This work was supported in part by grant HL 60301 from the National Institutes of Health.]

A new method for estimation of velocity vectors

The paper describes a new method for determining the velocity vector of a remotely sensed object using either sound or electromagnetic radiation. The movement of the object is determined from a field with spatial oscillations in both the axial direction of the transducer and in one or two directions transverse to the axial direction. By using a number of pulse emissions, the inter-pulse movement can be estimated and the velocity found from the estimated movement and the time between pulses. The method is based on the principle of using transverse spatial modulation for making the received signal influenced by transverse motion. Such a transverse modulation can be generated by using apodization on individual transducer array elements together with a special focusing scheme. A method for making such a field is presented along with a suitable two-dimensional velocity estimator. An implementation usable in medical ultrasound is described, and simulated results are presented. Simulation results for a flow of 1 m/s in a tube rotated in the image plane at specific angles (0, 15, 35, 55, 75, and 90 degrees) are made and characterized by the estimated mean value, estimated angle, and the standard deviation in the lateral and longitudinal direction. The average performance of the estimates for all angles is: mean velocity 0.99 m/s, longitudinal S.D. 0.015 m/s, and lateral S.D. 0.196 m/s. For flow parallel to the transducer the results are: mean velocity 0.95 m/s, angle 0.10, longitudinal S.D. 0.020 m/s, and lateral S.D. 0.172 m/s.

Developments in cardiovascular ultrasound: Part 1: Signal processing and instrumentation.

One of the major contributions to the improvement of spectral Doppler and colour flow imaging instruments has been the development of advanced signal-processing techniques made possible by increasing computing power. Model-based or parametric spectral estimators, time-frequency transforms, station-arising algorithms and spectral width correction techniques have been investigated as possible improvements on the FFT-based estimators currently used for real-time spectral estimation of Doppler signals. In colour flow imaging some improvement on velocity estimation accuracy has been achieved by the use of new algorithms but at the expense of increased computational complexity compared with the conventional autocorrelation method. Polynomial filters have been demonstrated to have some advantages over IIR filters for stationary echo cancellation. Several methods of velocity vector estimation to overcome the problem of angle dependence have been studied, including 2D feature tracking, two and three beam approaches and the use of spectral width in addition to mean frequency. 3D data acquisition and display and Doppler power imaging have also been investigated. The use of harmonic imaging, using the second harmonic generated by encapsulated bubble contrast media, seems promising particularly for imaging slow flow. Parallel image data acquisition using non-sequential scanning or broad beam transmission, followed by simultaneous reception along a number of beams, has been studied to speed up 'real-time' imaging.

Estimation of local image velocity vectors by using a sequence of local motion signals

Estimation of local image velocity vectors by using a sequence of local motion signals

2702 Estimation of local image velocity vectors by using a sequence of local motion signals

2702 Estimation of local image velocity vectors by using a sequence of local motion signals

3-D flow velocity vector estimation with a triple-beam lens transducer-experimental results

Current commercial ultrasound blood flow measurement systems only measure the axial component of the true blood flow velocity vector. In order to overcome this limitation, a technique which tracks blood cell scatterers as they move between three ultrasound beams has been developed. With this technique, the entire 3-D blood flow velocity vector can be estimated. Previous work has presented the theory behind the technique, lens transducer design and construction, as well as results of computer simulations and preliminary experimental results. This work presents the first experimental results obtained with a prototype system for continuous, fully developed flow in a flow phantom under a wide range of flow rates and flow directions. The results indicate that the accurate measurement of the 3-D flow velocity vector using this technique is possible.

Motion compensated image reconstruction and holographic Doppler velocimetry using an encoded wavefront

In this paper, an image reconstruction method for relatively moving targets with acoustical holography or a synthetic aperture focusing technique is proposed. A high-speed imaging system using transmitting pulses modulated with a system of Walsh functions was proposed by the authors. The method, which utilizes multiplex transmission, is called encoded wavefront transmission. Moving targets are simultaneously observed with a multiple transmission of pulses modulated by the Walsh functions. For each repetition period, a 3-D image is reconstructed. From a sequence of the reconstructed images, the relative velocity is estimated. Then the images are combined to a single motion compensated image. In the paper, the influence of the quantization of delay on the quality of reconstructed images is discussed. Allowable errors of velocity estimation are evaluated using computer simulations. Also discussed are the velocity vector estimation algorithms and the feasibility of this method to a ‘‘Holographic Doppler Velocimetry,’’ which visualizes the spatial distribution of the velocity vector. The experimental results demonstrate the ability of the method for a simple moving object.

Demonstration of three-dimensional vector flow estimation using bandwidth and two transducers on a flow phantom

A method of performing three-dimensional (3-D) velocity vector estimation with two transducers is demonstrated on a flow phantom using the Doppler spectra's mean frequencies and bandwidths. The results are compared with 3-D vector estimates computed from Doppler mean frequencies obtained with a five-transducer system. It is shown that the two-transducer vector Doppler system which uses bandwidth can improve on the accuracy of a three-transducer vector Doppler system which relies only on Doppler mean frequencies.

Estimating the velocity vector of fast moving sound source exploiting the retardation effect

The radiated noise of moving sound sources can be used to detect and localize these objects. Using microphone arrays with apertures comparing to the wavelength of the received signals, localization and velocity vector estimation will generally be done by means of triangulation. In this presentation it will be shown that, under certain conditions concerning the parameters of motion, the velocity vector itself (and not only the angular velocity) can be reconstructed using only the correlation measurements of one microphone array consisting of four microphones. The microphones of the array form three noncollinear bases with base lengths on the order of 0.5 m. The additional information needed results form the retardation effect. The retardation effect is a consequence of the finite signal velocity, and results in a mismatch between the indicated and the real target position if the target is moving. It becomes important at speeds of the sound source comparing to the signal propagation speed. On the basis of f...