A new high resolution color flow system using an eigendecomposition-based adaptive filter for clutter rejection

We present a new signal processing strategy for high frequency color flow mapping in moving tissue environments. A new application of an eigendecomposition-based clutter rejection filter is presented with modifications to deal with high blood-to-clutter ratios (BCR). Additionally, a new method for correcting blood velocity estimates with an estimated tissue motion profile is detailed. The performance of the clutter filter and velocity estimation strategies is quantified using a new swept-scan signal model. In vivo color flow images are presented to illustrate the potential of the system for mapping blood flow in the microcirculation with external tissue motion.     

A new high resolution color flow system using an eigendecomposition-based adaptive filter for clutter rejection

We present a new signal processing strategy for high frequency color flow mapping in moving tissue environments. A new application of an eigendecomposition-based clutter rejection filter is presented with modifications to deal with high blood-to-clutter ratios (BCR). Additionally, a new method for correcting blood velocity estimates with an estimated tissue motion profile is detailed. The performance of the clutter filter and velocity estimation strategies is quantified using a new swept-scan signal model. In vivo color flow images are presented to illustrate the potential of the system for mapping blood flow in the microcirculation with external tissue motion.     

Clutter filters adapted to tissue motion in ultrasound color flow imaging

The quality of ultrasound color flow images is highly dependent on sufficient attenuation of the clutter signals originating from stationary and slowly moving tissue. Without sufficient clutter rejection, the detection of low velocity blood flow will be poor, and the velocity estimates will have a large bias. In some situations, e.g., when imaging the coronary arteries or when the operator moves the probe in search for small vessels, there is considerable movement of tissue. It has been suggested that clutter rejection can be improved by mixing down the signal with an estimate of the mean frequency prior to high pass filtering. In this paper, we compare this algorithm with several other adaptive clutter filtering algorithms using both experimental data and simulations. We found that realistic accelerations of the tissue have a large effect on the clutter rejection. The best results were obtained by mixing down the signal with non-constant phase increments estimated from the signal. This adapted the filter to a possibly accelerated tissue motion and produced a significant improvement in clutter rejection     

Optimal velocity estimation in ultrasound color flow imaging in presence of clutter

In color flow imaging (CFI), the rejection of tissue clutter signal is treated separately from blood velocity estimation by high-pass filtering the received Doppler signal. The complete suppression of clutter is then difficult to achieve without affecting the subsequent velocity estimates. In this work, a different approach to velocity estimation is investigated, based on a statistical model of the signal from both clutter and blood. An analytic expression for the Cramer-Rao lower bound (CRLB) is developed, and used to determine the existence of an efficient maximum likelihood estimator (MLE) of blood velocity in CFI when assuming full knowledge of the clutter statistics. We further simulate and compare the performance of the MLE to that of the autocorrelation method (ACM) using finite-impulse response (FIR) and polynomial regression clutter filters. Two signal scenarios are simulated, representing a central and peripheral vessel. Simulations showed that, by including 3-9 (independent) spatial points, the MLE variance approached the CRLB in both scenarios. The ACM was approximately unbiased only for the central scenario in the clutter filter pass band, then with a variance of up to four times the CRLB. The ACM suffered from a severe bias in the filter transition region, and a significant performance gain was achieved here using the MLE. For practical use, the clutter properties must be estimated. We finally replaced the known clutter statistics with an estimate obtained from low-rank approximations of the received sample correlation matrix. Used in the model-based framework, this method came close to the performance of the MLE, and it may be an important step toward a practical model-based estimator, including tissue clutter with optimal performance.     

Clutter filter design for ultrasound color flow imaging

For ultrasound color flow images with high quality, it is important to suppress the clutter signals originating from stationary and slowly moving tissue sufficiently. Without sufficient clutter rejection, low velocity blood flow cannot be measured, and estimates of higher velocities will have a large bias. The small number of samples available (8 to 16) makes clutter filtering in color flow imaging a challenging problem. In this paper, we review and analyze three classes of filters: finite impulse response (FIR), infinite impulse response (IIR), and regression filters. The quality of the filters was assessed based on the frequency response, as well as on the bias and variance of a mean blood velocity estimator using an autocorrelation technique. For FIR filters, the frequency response was improved by allowing a non-linear phase response. By estimating the mean blood flow velocity from two vectors filtered in the forward and backward direction, respectively, the standard deviation was significantly lower with a minimum phase filter than with a linear phase filter. For IIR filters applied to short signals, the transient part of the output signal is important. We analyzed zero, step, and projection initialization, and found that projection initialization gave the best filters. For regression filters, polynomial basis functions provide effective clutter suppression. The best filters from each of the three classes gave comparable bias and variance of the mean blood velocity estimates. However, polynomial regression filters and projection-initialized IIR filters had a slightly better frequency response than could be obtained with FIR filters     

Estimation of mean frequency and variance of ultrasonic Doppler signal by using second-order autoregressive model

In order to estimate the mean frequency and variance of the diagnostic ultrasound Doppler signal in the presence of clutter noise, a new estimator using a second-order autoregressive (AR) model, called the AR estimator, is proposed. The sampled signal that contains information of both the Doppler signal and clutter is described by the second-order AR model with two poles. The mean frequency and variance of a unidirectional Doppler signal can be estimated, respectively, from the phase and the magnitude of the pole, with larger phase between the two poles. If the clutter is not completely rejected, all conventional estimators, including the autocorrelation (AC) estimator, result in erroneous estimations for the mean frequency and variance of the Doppler signal, whereas the AR estimator gives an accurate estimation. In the absence of clutter, however, the performance of both the AC and AR estimators are similar. If the blood flows in both directions in a sample volume and the clutter is rejected to the extent that it no longer obscures the Doppler signal, the proposed method can estimate simultaneously the mean frequencies and variances of both the forward and reverse blood flows. The performance of the proposed AR estimator was compared with that of the AC estimator by computer simulations and experiments, and it was found that when the number of available sampled data is small, the AR estimator does not require the use of a clutter filter, which simplifies Doppler signal detection.     

Clutter rejection filters in color flow imaging: a theoretical approach

A general class of linear clutter rejection filters is described, covering the commonly used filter types including FIR/IIR filters with linear initialization, as well as regression filters, where the clutter component is estimated by least square curve fitting. The filter can be described by a complex valued matrix, and a frequency response is defined. However, in contrast to a time invariant filter, the general linear filter may create frequency components which are not present in the input signal. This produces bias in the velocity and velocity spread estimates. It is shown that the clutter filter effect on the autocorrelation estimates can be described by a frequency domain transfer function, but unlike time invariant filters, the transfer function is different for each temporal lag of the autocorrelation function. Using a two dimensional (axial and temporal dimension) model of the received signal, the bias in velocity and velocity spread is quantified, both for the autocorrelation algorithm and the time shift cross-correlation estimator. Theoretical expressions, as well as numerical examples are given.     

Single-ensemble-based eigen-processing methods for color flow imaging--Part I. The Hankel-SVD filter

Because of their adaptability to the slow-time signal contents, eigen-based filters have shown potential in improving the flow detection performance of color flow images. This paper proposes a new eigen-based filter called the Hankel-SVD filter that is intended to process each slowtime ensemble individually. The new filter is derived using the notion of principal Hankel component analysis, and it achieves clutter suppression by retaining only the principal components whose order is greater than the clutter eigen-space dimension estimated from a frequency based analysis algorithm. To assess its efficacy, the Hankel-SVD filter was first applied to synthetic slow-time data (ensemble size: 10) simulated from two different sets of flow parameters that model: 1) arterial imaging (blood velocity: 0 to 38.5 cm/s, tissue motion: up to 2 mm/s, transmit frequency: 5 MHz, pulse repetition period: 0.4 ms) and 2) deep vessel imaging (blood velocity: 0 to 19.2 cm/s, tissue motion: up to 2 cm/s, transmit frequency: 2 MHz, pulse repetition period: 2.0 ms). In the simulation analysis, the post-filter clutter-to- blood signal ratio (CBR) was computed as a function of blood velocity. Results show that for the same effective stopband size (50 Hz), the Hankel-SVD filter has a narrower transition region in the post-filter CBR curve than that of another type of adaptive filter called the clutter-downmixing filter. The practical efficacy of the proposed filter was tested by application to in vivo color flow data obtained from the human carotid arteries (transmit frequency: 4 MHz, pulse repetition period: 0.333 ms, ensemble size: 10). The resulting power images show that the Hankel-SVD filter can better distinguish between blood and moving-tissue regions (about 9 dB separation in power) than the clutter-downmixing filter and a fixed-rank multi ensemble-based eigen-filter (which showed a 2 to 3 dB separation).     

Target velocity estimation with FM and PW echo ranging Doppler systems I. Signal analysis

The theoretical foundation is presented for velocity estimation with a pulsed wave (PW) Doppler system transmitting linear FM signals. The Doppler system possesses echo ranging capabilities and is evaluated in the context of Doppler ultrasound for blood velocity measurement. The FM excitation signal is formulated and the received signal is derived for a single moving particle. This signal is similar to the transmitted signal, but with modified parameters due to Doppler effect and range. The demodulated received signal is subsequently derived and analyzed. It is shown that, due to the Doppler effect, this is a linear sweep signal as well. The velocity and range information obtainable from one and two consecutively received signals are described. The latter case establishes the basis for an FM Doppler system for blood velocity measurements.     

Extraction of mixed-order multicomponent ship target signals from broadened sea clutter in bistatic shipborne surface wave radar

A dynamic geometry model was built to describe the Doppler-broadening characteristics of the first-order Bragg lines for bistatic shipborne surface wave radar. They are time-varying because the Doppler frequency shifts of sea echoes are simultaneously modulated by the velocity components projected from the unavoidably different motions of both platforms, which is more complex than its counterpart in the monostatic mode. The geometrical relation is used to obtain the received signal model: strong first-order sea clutter interferences and submerged ship targets with constant and non-constant speeds are considered as mixed-order multicomponent polynomial-phase signals (mc-PPSs) and both second-order sea clutter continuum and atmospheric noise as additive noise. Then, a scheme based on the product high-order ambiguity function is proposed to extract the targets; it is a recursive procedure in which the first-order sea clutter is removed by an existing time-space cascaded filtering method. Monte Carlo simulations show the validity and efficiency of the proposed scheme.     

光子多普勒测速系统信号解调方法比较

光子多普勒测速系统具有抗干扰能力强、测速范围大等优点,适用于信噪比低、信号质量差的测量场合。介绍光子多普勒测速系统的工作原理,详细阐述常用的四种信号解调方法——条纹法、相位解调法、短时傅里叶变换法、小波变换法的原理、特点和近几年的研究现状。利用上述四种信号解调方法对简谐振动调制的多普勒信号进行解调仿真,直观地展示不同信号解调方法的优缺点和适用性。实验结果表明,相位解调法最适合用于光子多普勒测速系统振动信号解调。最后讨论了采用递归希尔伯特变换的方法减小相位解调法的正交性误差的可行性,通过仿真实验验证了此方法的有效性。     

A new pulsed wave Doppler ultrasound system to measure bloodvelocities beyond the Nyquist limit

Conventional pulsed wave (PW) Doppler ultrasound systems measure blood velocities unambiguously as long as the velocities are less than the Nyquist velocity. Here, a new PW Doppler ultrasound system is described, which can measure velocities up to 4.5 times higher than the Nyquist velocity. The new PW system presented here utilizes two ultrasound carrier frequencies, such that an appropriate processing of the Doppler frequencies results in an extended mean-velocity range. With this extended mean-velocity information, the complex Doppler signal is interpolated to reconstruct aliased Doppler spectra. The interpolation algorithm has been tested by computer simulations demonstrating the capabilities and limits. The integration into a commercial Doppler scanner allowed the evaluation of the new PW system in real time. In vitro and in vivo tests demonstrate the effective reconstruction of highly aliased Doppler spectra     

Two-dimensional pulse-to-pulse canceller of ground clutter in airborne radar

It is well known that in the airborne radar, the location of the ground clutter spectrum in the angle- Doppler space is dependent mainly on the platform velocity and radar parameters. The authors propose a two-dimensional pulse-to-pulse canceller (TDPC) that can make full use of such prior information. The more detailed formulations of the ground clutter model and the signal model are given in a matrix?vector form. The least-squares-typical cost function associated with the filter coefficient matrix of the TDPC is established on the basis of the ground clutter model and the signal model. Like the classical displaced phase centre antenna (DPCA) processing, the proposed TDPC is also a spatial-temporal suppressor of ground clutter and can decrease the ground clutter signals, even though the DPCA condition is not satisfied. The proposed TDPC can also be used as an efficient pre-filtering tool before the conventional moving target indication (MTI) processing and the classical adaptive processing. Moreover, if only the TDPC plus the conventional MTI is used, it takes less computational time than the adaptive canceller. Experimental results show that the proposed TDPC has the satisfactory ground clutter suppression capability by using both simulated data and measured data.     

A new time-domain narrowband velocity estimation technique for Doppler ultrasound flow imaging. II. Comparative performance assessment

For pt.I see ibid., vol.45, no.4, pp.939-54 (1998). The statistical performance of the new 2-D narrowband time-domain root-MUSIC blood velocity estimator described previously is evaluated using both simulated and flow phantom wideband (50% fractional bandwidth) ultrasonic data. Comparisons are made with the standard 1-D Kasai estimator and two other wideband strategies: the time domain correlator and the wideband point maximum likelihood estimator. A special case of the root-MUSIC, the "spatial" Kasai, is also considered. Simulation and flow phantom results indicate that the root-MUSIC blood velocity estimator displays a superior ability to reconstruct spatial blood velocity information under a wide range of operating conditions. The root-MUSIC mode velocity estimator can be extended to effectively remove the clutter component from the sample volume data. A bimodal velocity estimator is formed by processing the signal subspace spanned by the eigenvectors corresponding to the two largest eigenvalues of the Doppler correlation matrix. To test this scheme, in vivo common carotid flow complex Doppler data was obtained from a commercially available color flow imaging system. Velocity estimates were made using a reduced form of this data corresponding to higher frame rates. The extended root-MUSIC approach was found to produce superior results when compared to both 1- and 2-D Kasai-type estimators that used initialized clutter filters. The results obtained using simulated, flow phantom, and in vivo data suggest that increased sensitivity as well as effective clutter suppression can be achieved using the root-MUSIC technique, and this may be particularly important for wideband high frame rate imaging applications.     

Adaptive clutter rejection for ultrasound color flow imaging based on recursive eigendecomposition

In the conventional eigenfilter used to reject clutter components of ultrasound color flow imaging, input samples are required to be statistically stationary. However, clutter movements may vary over the depth of the imaged area, which makes the eigenfilter less efficient. In the current study, a novel clutter rejection method is proposed based on the recursive eigendecomposition algorithm. In this method, the current eigenvector matrix of the ultrasound echo correlation matrix, which will be used to construct the clutter subspace, is determined by previous eigenvector matrices and the current input. After the estimated clutter signal is obtained by projecting the original input into the clutter space, each filtered output is eventually obtained by subtracting the estimated clutter signal from the original input. This procedure is iterated for each sample volume along the depth. During the updating process, a forgetting factor is introduced to determine proper weights for different inputs. Simulated data in 3 situations and in vivo data collected from human carotid arteries are used to compare the proposed method with other popular clutter filters. Results show that the proposed method can achieve the most accurate velocity profiles in all simulation situations and introduces the fewest velocity artifacts in the tissue region in the in vivo experiment.     

Spectral Doppler estimation utilizing 2-D spatial information and adaptive signal processing

The trade-off between temporal and spectral resolution in conventional pulsed wave (PW) Doppler may limit duplex/triplex quality and the depiction of rapid flow events. It is therefore desirable to reduce the required observation window (OW) of the Doppler signal while preserving the frequency resolution. This work investigates how the required observation time can be reduced by adaptive spectral estimation utilizing 2-D spatial information obtained by parallel receive beamforming. Four adaptive estimation techniques were investigated, the power spectral Capon (PSC) method, the amplitude and phase estimation (APES) technique, multiple signal classification (MUSIC), and a projection-based version of the Capon technique. By averaging radially and laterally, the required covariance matrix could successfully be estimated without temporal averaging. Useful PW spectra of high resolution and contrast could be generated from ensembles corresponding to those used in color flow imaging (CFI; OW = 10). For a given OW, the frequency resolution could be increased compared with the Welch approach, in cases in which the transit time was higher or comparable to the observation time. In such cases, using short or long pulses with unfocused or focused transmit, an increase in temporal resolution of up to 4 to 6 times could be obtained in in vivo examples. It was further shown that by using adaptive signal processing, velocity spectra may be generated without high-pass filtering the Doppler signal. With the proposed approach, spectra retrospectively calculated from CFI may become useful for unfocused as well as focused imaging. This application may provide new clinical information by inspection of velocity spectra simultaneously from several spatial locations.     

A new wideband spread target maximum likelihood estimator for blood velocity estimation. I. Theory

The derivation and theoretical evaluation of new wideband maximum-likelihood strategies for the estimation of blood velocity using acoustic signals are presented. A model for the received signal from blood scatterers, using a train of short wideband pulses, is described. Evaluation of the autocorrelation of the signal based on this model shows that the magnitude, periodicity, and phase of the autocorrelation are affected by the mean scatterer velocity and the presence of a velocity spread target. New velocity estimators are then derived that exploit the effect of the scatterer velocity on both the signal delay and the shift in frequency. The wideband range spread estimator is derived using a statistical model of the target. Based on the point target assumption, a simpler wideband maximum-likelihood estimator is also obtained. These new estimation strategies are analyzed for their local and global performance. Evaluation of the Cramer-Rao bound shows that the bound on the estimator variance is reduced using these estimators, in comparison with narrowband strategies. In order to study global accuracy, the expected estimator output is evaluated, and it is determined that the width of the mainlobe is reduced. In addition, it is shown that the height of subsidiary velocity peaks is reduced through the use of these new estimators.     

Effect of the beam-vessel angle on the received acoustic signalfrom blood

In order to explore the feasibility of algorithms to determine the three dimensional (3D) velocity magnitude from the received ultrasonic blood echo from a single line of sight, the signal from small sample volumes is studied as a function of beam-vessel angle. As opposed to previous treatments of the effect of the beam-vessel angle on the received acoustic signal, a wideband signal is transmitted and the returned signal in each sample volume is analyzed. High-resolution experimental M-mode images of radio-frequency (rf) echo signals are used to visualize the flow in individual regions of interest. These experiments confirm the predictions of a theoretical model for the signal and its second moment. It is shown that the two major effects limiting the correlated signal interval are the spread of axial velocities within the sample volume and the transit time across the lateral beam width. Particularly for small beam-vessel angles, the spread of velocities limits the correlated signal interval. In addition, the experimental results demonstrate that accurate velocity estimation for low volume flow rates and particularly for large beam-vessel angles may involve detection of changes in the correlation magnitude. For low volume flow rates, the shape of the correlation surface can be affected by small regions of blood with a strong scattering intensity located near the initial region of interest     

板振动的无需次级通道建模的分散式前馈控制方法研究

本文针对板的振动,提出了一种无需次级通道建模的分散式前馈控制方法。该前馈控制方法不需要结构的物理信息,并且能够控制板在非共振频率处的线谱振动。采用压电片和加速度计分别作为执行和传感元件,建立了简支板振动主动控制的理论模型和实验系统。提出了分散式前馈控制策略,并分析了无需次级通道建模的分散式前馈控制算法的稳定性。提出了一种内模滤波器将加速度信号转变为速度信号,并补偿抗混叠滤波器和平滑滤波器的频率响应,使执行器和传感器保持同位配置。通过仿真和实验验证了该算法的有效性。     

Approximate Cramer-Rao bound on Doppler error in correlation-processing relatively narrowband noise radar

Limitations on accuracy of Doppler estimation in continuous-wave noise radar with correlation processing are studied. Second-order properties of output of the correlation receiver are evaluated and an approximate Cramer-Rao bound on errors of Doppler measurement is derived. The accuracy of Doppler measurements is found to be affected by the following factors: power spectral density of noise signal, frequency response of the low-pass filter in correlator, observation time, velocity of the target and signal to noise ratio. It is shown that the random nature of the transmitted signal induces additional fluctuations at the output of correlator which limit the accuracy even in the infinite signal to noise case. Qualitative extension of the results to a case covering multiple targets and clutter is made. It is argued that the performance will decrease and that increasing transmitted power may not provide significant improvement when clutter is present.