Low-order AR models for mean and maximum frequency estimation in the context of Doppler color flow mapping

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.

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.

Color flow mapping

Color flow mapping systems have become widely used in the short time since their development. These systems overlay a pseudo-color velocity map upon the gray-scale two-dimensional image. Between 4 and 16 pulses are directed to each line-of-sight, and this requirement reduces the frame rate in comparison with the gray-scale image. Other limitations of color flow mapping include its ability to estimate only the velocity toward or away from the transducer and an increase in the variance in comparison with spectral Doppler. Potential artifacts include aliased velocities and the detection of flow in hypoechoic or hyperechoic nonvascular structures. Clinical applications include cardiology, studies of the abdominal and peripheral vasculature, evaluation of organ perfusion and the differentiation of tumors. Most current systems use narrowband estimators that examine a fixed sample volume and detect a change in phase between two pulses. Wideband estimators that can track red blood cells in two or three dimensions are under evaluation. Narrowband estimators, including the autocorrelator, the short Fourier transform and second order autoregressive filters, are compared with wideband estimators including cross-correlation, sum-absolute-difference and the wideband maximum likelihood estimator. Because the intensity of blood echoes is far smaller than echoes from surrounding tissue, high pass filters have been developed that can reject the larger signal from tissue using the return from a small number of pulses. Other areas of research include strategies for flow estimation with contrast agents, three-dimensional color flow mapping and power Doppler flow mapping.

Recent developments in breast imaging

A review of breast imaging has already appeared in 1982 in this journal. Consequently, the present article concentrates on a discussion of only those developments of a more recent nature. Although the emphasis is placed on the physical aspects of the different imaging methods concerned, the essential factors relating to the clinical background and the associated radiation risk are also outlined. The completeness of detail depends on the present clinical importance of the method under discussion. X-ray mammography, which is still the most important breast imaging technique and has proved to be an effective method for breast cancer screening, is therefore treated in greater detail. Since the early 1980s, ultrasound B-mode scanning has evolved to an indispensable adjunct to x-ray mammography. For Doppler sonography, diaphanography, contrast-enhanced MRI, CT and DSA, the visualization of a tumour depends essentially on the enhanced vascularity of the lesion. Whether this will prove to be a reliable indicator for malignancy remains to be shown in controlled clinical studies. Common to all imaging systems is the increasing use of digital methods for signal processing, which also offers the possibility of computer-aided diagnosis by texture analysis and pattern recognition.

Cost/benefit criterion for selection of pulsed Doppler ultrasound spectral mean frequency and bandwidth estimators

A flexible selection criterion for spectral estimators based on the weighted statistical accuracy (benefit) of estimation of decisive spectral parameters under the constraint of low computational complexity (cost) is proposed. This new cost/benefit criterion also selects the model order for parametric spectral estimators-selecting model orders significantly lower than those determined by accepted criteria. The importance of different Doppler signal parameters (e.g., mean frequency and spectral bandwidth) and their accuracy of estimation is incorporated by the use of weighting factors. The use of this method with simulated Doppler signals led to the selection of the modified covariance Alt estimator.

A comparison of colour flow imaging algorithms

In this paper we will present and explain coherently the two main algorithms which are currently used in commercial colour flow imaging systems, namely the frequency domain based autocorrelation algorithm and the time domain based cross correlation algorithm. The autocorrelation algorithm is a robust optimum mean frequency baseband estimator, for both high and low signal to noise ratio (SNR). Its main disadvantage is its aliasing problem. However the cross correlation algorithm does not suffer from this problem, and this has been one of the main reasons for its development. The mathematics behind these two algorithms and the general data processing steps used for their implementation will be also presented. The subject of clutter removal filtering will be discussed and valuable points will be made. A practical relevant approach on how to discriminate between wanted blood flow related estimates and unwanted false estimates due to noise will be presented. On the aliasing problem of the autocorrelation algorithm, a promising solution known as spatial tracking of estimated mean frequency does exist, which will be also introduced in detail. Towards the end of this paper other algorithms, which are currently the subject of research and have potential for development, will be discussed.