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     

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.     

Real-time adaptive clutter rejection filtering in color flow imaging using power method iterations

We propose a new algorithm for real-time, adaptive-clutter-rejection filtering in ultrasound color flow imaging (CFI) and related techniques. The algorithm is based on regression filtering using eigenvectors of the signal correlation matrix as a basis for representing clutter, a method that previously has been considered too computationally demanding for real-time processing in general CFI applications. The data acquisition and processing scheme introduced allows for a more localized sampling of the clutter statistics and, therefore, an improved clutter attenuation for lower filter orders. By using the iterative power method technique, the dominant eigenvalues and corresponding eigenvectors of the correlation matrix can be estimated efficiently, rendering real-time operation feasible on desktop computers. A new adaptive filter order algorithm is proposed that successfully estimates the proper dimension of the clutter basis, previously one of the major drawbacks of this clutter-rejection technique. The filter algorithm performance and computational demands has been compared to that of conventional clutter filters. Examples have been included which confirms that, by adapting the clutter-rejection filter to estimates of the clutter-signal statistics, improved attenuation of the clutter signal can be achieved in normal as well as more excessive cases of tissue movement and acceleration.     

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.     

Comparative analysis of low-pass filters for the demodulation ofprojected gratings in 3-D adaptive profilometry

In 3-D adaptive profilometry based on structured light projection, the choice of the low-pass filter to he used in the deformed pattern demodulation is crucial. In this paper, we have studied the performance of a typical finite impulse response (FIR) and of an infinite impulse response (IIR) Butterworth low-pass filter. Adaptiveness of the filters to both coarse and small variations of the grating frequency has been investigated. The ability of the filters to adapt to coarse changes of the grating frequency has been quantified in terms of their speed of synthesis, while the ability of the filters to tolerate small variations of the grating frequency has been quantified by measuring the residual phase errors. The analysis shows that the IIR Butterworth filter performs better than the FIR filter both in the coarse and in the fine grating frequency variation cases     

Adaptive clutter filtering based on sparse component analysis in ultrasound color flow imaging

An adaptive method based on the sparse component analysis is proposed for stronger clutter filtering in ultrasound color flow imaging (CFI). In the present method, the focal underdetermined system solver (FOCUSS) algorithm is employed, and the iteration of the algorithm is based on weighted norm minimization of the dependent variable with the weights being a function of the preceding iterative solutions. By finding the localized energy solution vector representing strong clutter components, the FOCUSS algorithm first extracts the clutter from the original signal. However, the different initialization of the basis function matrix has an impact on the filtering performance of FOCUSS algorithms. Thus, 2 FOCUSS clutter- filtering methods, the original and the modified, are obtained by initializing the basis function matrix using a predetermined set of monotone sinusoids and using the discrete Karhunen-Loeve transform (DKLT) and spatial averaging, respectively. Validation of 2 FOCUSS filtering methods has been performed through experimental tests, in which they were compared with several conventional clutter filters using simplistic simulated and gathered clinical data. The results demonstrate that 2 FOCUSS filtering methods can follow signal varying adaptively and perform clutter filtering effectively. Moreover, the modified method may obtain the further improved filtering performance and retain more blood flow information in regions close to vessel walls.     

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.     

Techniques for perfusion imaging with microbubble contrast agents

The acoustic properties of ultrasound contrast agents vary widely with agent composition and insonation conditions. For contrast imaging, methods are required to match RF and Doppler processing to each combination of transmission parameters and agent and tissue properties. We propose a method that uses the measured or modeled echoes from agent and tissue to specify directly the characteristics of RF and Doppler filters for contrast imaging. The proposed method is sufficiently general to cover most common imaging techniques including harmonic greyscale, Doppler, and pulse inversion imaging. Using this method, sample filters were designed to detect myocardial perfusion with the contrast agent Optison^TM (Mallinckrodt Medical, St. Louis, MO) under selected imaging conditions. Simplified power Doppler filtering, using a weighted sum of the Doppler samples, matched the performance of more complicated matrix filters. By coordinating the selection of RF and Doppler filters rather than designing these filters sequentially, agent-to-tissue contrast was increased by up to 3.9 dB. Under some conditions, fundamental RF filtering outperformed harmonic filtering for intermittent Doppler imaging     

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.     

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.     

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.     

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     

Real-time integration and differentiation of analog signals bymeans of digital filtering

A novel filter design method for broadband recursive digital integrators and differentiators is presented. The performance of the digital infinite-impulse response (IIR) filters designed with the method is compared with that of finite-impulse response (FIR) filters and that of classical numerical integration and differentiation. The common conviction that IIR filters with excellent amplitude characteristics always have poor phase behavior is refuted. It is shown that it is possible to design easily realizable IIR integrators and differentiators with an arbitrarily small amplitude and phase error. While there is no FIR alternative for IIR integrators, both FIR and IIR methods give competitive results for differentiators     

Application of the radon transform to detect small-targets in sea clutter

The authors present a novel and heuristic approach for the detection of low radar cross-section targets in high-resolution sea clutter. The proposed technique is based on the application of the Radon transform to range?time matrices formed by column-wise storage of consecutive range profiles. The objective of this paper is 2-fold: to analyse the effect of the transform on real high-resolution sea clutter and to describe a detection scheme based on the insight obtained. The proposed technique emulates the behaviour of traditional motion target detection algorithms without the need for reliable Doppler information. It also constitutes a powerful non-coherent integration strategy of the target?s energy along its specific path on the range?time plot. The performance of the detection technique has been tested against real high-resolution sea clutter data, acquired at the south coast of Spain with an in-house developed continuous wave linear frequency modulated millimetre-wave radar system. Monte Carlo simulations show a significant improvement over the conventional cell averaging constant false alarm rate schemes.     

Graphics Processing Unit-Based High-Frame-Rate Color Doppler Ultrasound Processing

Color Doppler ultrasound is a routinely used diagnostic tool for assessing blood flow information in real time. The required signal processing is computationally intensive, involving autocorrelation, linear filtering, median filtering, and thresholding. Because of the large amount of data and high computational requirement, color Doppler signal processing has been mainly implemented on custom-designed hardware, with software-based implementation - particularly on a general- purpose CPU - not being successful. In this paper, we describe the use of a graphics processing unit for implementing signal-processing algorithms for color Doppler ultrasound that achieves a frame rate of 160 fps for frames comprising 500 scan lines times 128 range samples, with each scan line being obtained from an ensemble size of 8 with an 8-tap FIR clutter filter.     

Hardware-efficient realization of a real-time ultrasonic target detection system using IIR filters - [correspondence]

In this study, we address the increased computational demands of a frequency-diverse ultrasonic target detection system by developing a zero-phase IIR (ZP-IIR) filter. Several ZP-IIR filter types including Chebyshev-I, Chebyshev- II, and Butterworth were analyzed for their detection performance. The 4th-order filters with 8-bit quantized coefficients are shown to improve the flaw-to-clutter ratio by approximately 10 dB. Furthermore, the reduced adder graph algorithm is used for a hardware realization of ZP-IIR filters that does not require any dedicated multipliers. A small number of coefficients inherent to IIR filters and their multiplierless implementation provide efficient architecture suitable for compact, real-time ultrasonic imaging devices.     

Complex correction of data acquisition channels using FIR equalizerfilters

The common conviction about FIR (finite impulse response) digital filters is that the number of necessary taps, to reach the same performance as provided by IIR (infinite impulse response) digital filters, is usually too large. Moreover, the standard FIR filter design algorithm (Remez exchange) allows the design of linear-phase filters only. Therefore, IIR filters are often preferred over FIR ones, without any further investigations. This paper presents a case study of complex (amplitude and phase) equalization of the passband of a commercial anti-aliasing filter. The novelty is the usage of an FIR filter for this purpose (or an FIR one, combined with a low-order IIR filter), and a thorough discussion of the special design aspects. It turns out that for the given anti-aliasing filter (a Cauer filter of order 11) an FIR filter of length 60···100 can perform as well as a 26/26 (numerator order/denominator order) IIR one. The properties are even better if a low-order IIR filter is used in combination with an FIR one (orders, e.g., 1/1+40/0). Because of the absence of stability problems and the ease of implementation, the use of FIR filters is suggested     

Asymptotic equivalence of some adaptive biquad notch filters

A diverse choice of biquad designs is available for adaptive notch filtering or line enhancement (ANF/ALE) applications. We consider one such biquad proposed over a decade ago by David and coworkers and show its equivalence to two other formulations in terms of their pole-zero pair locations in thez-plane. By equivalence, we imply that all these adaptive IIR filters possess comparable asymptotic performance. Further, a simple modification, involving only a normalizing factor, is seen to enhance the performance of this filter. This modified ANF/ALE design is then shown to be equivalent to two other recently proposed adaptive biquads.