A theoretical framework for performance characterization of elastography: the strain filter

This paper presents a theoretical framework for performance characterization in strain estimation, which includes the effect of signal decorrelation, quantization errors due to the finite temporal sampling rate, and electronic noise. An upper bound on the performance of the strain estimator in elastography is obtained from a strain filter constructed using these limits. The strain filter is a term used to describe the nonlinear filtering process in the strain domain (due to the ultrasound system and signal processing parameters) that allows the elastographic depiction of a limited range of strains from the compressed tissue. The strain filter predicts the elastogram quality by specifying the elastographic signal-to-noise ratio (SNR(e)), sensitivity, and the strain dynamic range at a given resolution. The dynamic range is limited by decorrelation errors for large tissue strain values, and electronic noise for low strain values. Tradeoffs between different techniques used to enhance elastogram image quality may also be analyzed using the strain filter.     

Estimation and reduction of decorrelation effect due to tissue lateral displacement in elastography

In cross-correlation based elastography, the quality of the strain image is degraded by the distortion of echo waveforms due to tissue axial and lateral displacement. To study the effects of tissue lateral displacement on echo decorrelation, a tissue axial stretching model is developed and a concept called correlation signal-to-noise ratio (CSNR) is introduced to quantify the decorrelation effect due to tissue lateral displacement. A computer simulation based on the tissue stretching model is carried out to study the influence of several important elastographic parameters on echo decorrelation due to tissue lateral displacement. Finally, guided by the CSNR concept, a 2-D spatial comprehensive cross-correlation method is proposed to reduce the decorrelation noise. Results indicate that CSNR can be used as a quality indicator of elastography and the 2-D spatial comprehensive cross-correlation method can effectively reduce the decorrelation noise while slightly decreasing the lateral resolution of the strain image     

Wavelet transform-based strain estimator for elastography

A new signal processing algorithm based on a wavelet transform (WT) is proposed for instantaneous strain estimation in acoustic elastography. The proposed estimator locally weighs ultrasonic echo signals acquired before tissue compression by a Gaussian window function and uses the resulting waveform as a mother wavelet to calculate the WT of the postcompression signal. From the location of the WT peak, strain is estimated in the time-frequency domain. Because of the additive noise in signals and the discrete sampling, errors are commonly made in estimating the strain. Statistics of these errors are analyzed theoretically to evaluate the performance of the proposed estimator. The strain estimates are found to be unbiased, but error variances depend on the signal properties (echo signal-to-noise ratio and bandwidth), signal processing parameter (time-bandwidth product), and the applied strain. The results are compared with those obtained from the conventional strain estimator based on time-delay estimates. The proposed estimator is shown to offer strain estimates with greater precision and potentially higher spatial resolution, dynamic range, and sensitivity at the expense of increased computation time.     

Noise reduction for ultrasonic elastography using transmit-side frequency compounding: a preliminary study

Ultrasonic elastography is an imaging technique providing information about the relative stiffness of biological tissues. In general, elastography suffers from noise artifacts, which degrade lesion detectability and increase the likelihood of misdiagnosis. This paper proposes a method called transmit- side frequency compounding for elastography (TSFC). Beamforming is modified to transmit frames with N alternating center frequencies. Pairs of frames with the same center frequency are used to calculate sub-elastograms that are then averaged to produce one compounded elastogram. Simulation results based on an uniformly elastic tissue model demonstrate the decorrelation among sub-elastograms and the improvement in elastographic signal-to-noise ratio (SNRe) achieved by compounding sub-elastograms. An elastic phantom experiment further validates the noise reduction obtained by the proposed technique.     

Three-dimensional tissue motion and its effect on image noise inelastography

In elastography both high correlation coefficient between pre- and post-compression RF signals and high applied strain are required to achieve the best quality in elastograms. Because the elastogram is computed using a 1-D cross-correlation technique applied to a 1-D ultrasound signal, it is assumed that tissue motion occurs only within the axis of compression (axis of the acoustic wave propagation), or at least that the scatterers remain within the acoustic beam during tissue motion. In practice, soft tissues are incompressible and, therefore, the lateral and elevational (out-of-plane) tissue strains are 50% of the applied strain. Therefore, tissue scatterers may move across the beam due to the applied compression. In this paper we address the degradation of the elastographic quality due to the lateral and elevational motion of the scatterers in uniformly elastic media. A full 3-D model predicting the correlation coefficient as measured using 1-D cross-correlations is proposed. It is shown that the signal-to-noise ratio in elastograms (SNR_e) is nonstationary, and that it depends on the beamwidth and on the applied strain. In order to achieve a higher stationary SNR_e, it is proposed to confine the tissue in the lateral direction. Phantom experiments are used to corroborate the theoretical developments     

Complex principal components for robust motion estimation

Bias and variance errors in motion estimation result from electronic noise, decorrelation, aliasing, and inherent algorithm limitations. Unlike most error sources, decorrelation is coherent over time and has the same power spectrum as the signal. Thus, reducing decorrelation is impossible through frequency domain filtering or simple averaging and must be achieved through other methods. In this paper, we present a novel motion estimator, termed the principal component displacement estimator (PCDE), which takes advantage of the signal separation capabilities of principal component analysis (PCA) to reject decorrelation and noise. Furthermore, PCDE only requires the computation of a single principal component, enabling computational speed that is on the same order of magnitude or faster than the commonly used Loupas algorithm. Unlike prior PCA strategies, PCDE uses complex data to generate motion estimates using only a single principal component. The use of complex echo data is critical because it allows for separation of signal components based on motion, which is revealed through phase changes of the complex principal components. PCDE operates on the assumption that the signal component of interest is also the most energetic component in an ensemble of echo data. This assumption holds in most clinical ultrasound environments. However, in environments where electronic noise SNR is less than 0 dB or in blood flow data for which the wall signal dominates the signal from blood flow, the calculation of more than one PC is required to obtain the signal of interest. We simulated synthetic ultrasound data to assess the performance of PCDE over a wide range of imaging conditions and in the presence of decorrelation and additive noise. Under typical ultrasonic elasticity imaging conditions (0.98 signal correlation, 25 dB SNR, 1 sample shift), PCDE decreased estimation bias by more than 10% and standard deviation by more than 30% compared with the Loupas method and normalized cross-correlation with cosine fitting (NC CF). More modest gains were observed relative to spline-based time delay estimation (sTDE). PCDE was also tested on experimental elastography data. Compressions of approximately 1.5% were applied to a CIRS elastography phantom with embedded 10.4-mm-diameter lesions that had moduli contrasts of -9.2, -5.9, and 12.0 dB. The standard deviation of displacement estimates was reduced by at least 67% in homogeneous regions at 35 to 40 mm in depth with respect to estimates produced by Loupas, NC CF, and sTDE. Greater improvements in CNR and displacement standard deviation were observed at larger depths where speckle decorrelation and other noise sources were more significant.     

An adaptive strain estimator for elastography

Elastography is based on the estimation of strain due to applied tissue compression. In conventional elastography, strain is computed from the gradient of the displacement estimates between gated pre- and postcompression echo signals. Gradient-based estimation methods are known to be susceptible to noise. In elastography, in addition to the electronic noise, a principal source of estimation error is the decorrelation of the echo signal as a result of tissue compression (decorrelation noise). Temporal stretching of postcompression signals previously was shown to reduce the decorrelation noise. In this paper, we introduce a novel estimator that uses the stretch factor itself as an estimator of the strain. It uses an iterative algorithm that adaptively maximises the correlation between the pre- and postcompression echo signals by appropriately stretching the latter. We investigate the performance of this adaptive strain estimator using simulated and experimental data. The estimator has exhibited a vastly superior performance compared with the conventional gradient-based estimator.     

广义互相关时延估计声定位算法研究

针对地面目标声定位因信噪比较低而定位精度差的现象,提出了基于广义互相关法的声定位系统,根据平面四元法目标定位计算式,研究了广义互相关算法在实际中的应用。环境噪声、军事目标声和民用目标声频谱范围大多集中,即出现目标声会与背景噪声高度重合的情况,发现一般加窗滤波法在降低噪声的同时亦会将目标声强度大大削弱,而广义互相关时延估计法是通过计算两路信号互相关函数的最大值而求得时延差,其精度高、稳定性好。通过计算机仿真得到在信噪比较低的情况下,加窗滤波因大大削弱目标声强度而造成定位精度较低,而利用广义互相关方法可得到较为精确的声定位坐标。     

Bayesian and least squares approaches to ultrasonic scatterer size image formation

Scatterer size images can be used to describe renal microstructure and function in vivo. Such information may facilitate early detection of disease processes. When high range resolution is required, however, it is necessary to analyze short data segments. Periodogram-based maximum likelihood (ML) techniques for scatterer size estimation are limited in these situations by noise and range-gate artifacts. Moreover, when the input signal-to-noise ratio (SNR) of the echo signal is small, performance is further degraded. If accurate prior information about the approximate properties of the object is available, it can be incorporated into the solution to improve the estimates by reducing the number of possible solutions. In this paper, use of prior knowledge in scatterer size image formation is investigated. A maximum a posteriori (MAP) estimator, based on a random-object model, and an iterative constrained least squares (CLS) estimator, based on a deterministic-object model, are designed. Their performances and that of a Wiener filter are compared with the ML technique as a function of gate duration and SNR.     

Analysis of correlation coefficient filtering in elasticity imaging

Correlation-based speckle tracking methods are commonly used in elasticity imaging to estimate displacements. In the presence of local strain, a larger window size results in larger displacement error. To reduce tracking error, we proposed a short correlation window followed by a correlation coefficient filter. Although simulation and experimental results demonstrated the efficacy of the method, it was not clear why correlation coefficient filtering reduces tracking error since tracking error increases if normalization before filtering is not applied. In this paper, we analyzed tracking errors by estimating phase variances of the cross-correlation function and the correlation coefficient at the true time lag based on statistical properties of these functions' real and imaginary parts. The role of normalization is clarified by identifying the effect of the cross-correlation function's amplitude fluctuation on the function's imaginary part. Furthermore, we present analytic forms for predicting axial displacement error as a function of strain, system parameters (signal-to-noise ratio, center frequency, and signal and noise bandwidths), and tracking parameters (window and filter sizes) for cases with and without normalization before filtering. Simulation results correspond to theory well for both noise-free cases and general cases with an empirical correction term included for strains up to 4%.     

Subtraction elastography for the evaluation of ablation-induced lesions: a feasibility study

Different noninvasive or minimally invasive therapeutic ablation procedures can produce tissue necrosis associated with local-stiffness increase. Although elastography has been proved as a potential evaluation tool for many kinds of ablation-induced lesions, the application of subtraction technique in elastography to enhance the visualization of the ablation lesions has rarely been reported. In this paper, subtraction elastography is proposed to evaluate the ablation-induced lesions. Three models are constructed to simulate different kinds of ablated inclusions. The simulation results showed that subtraction elastography is superior to conventional elastography in detecting the ablation-induced lesions with higher signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR). The artifacts induced by elastographic signal processing algorithms can be largely reduced in subtraction elastography. In addition, subtraction elastography is less influenced by the stiff background and can provide more reliable boundary information about the lesion than conventional elastography. Furthermore, the feasibility of subtraction elastography is validated by an in vitro experiment of ethanol-induced hepatic lesions. The preliminary results of this work suggest that subtraction elastography may be a good option for the evaluation of ablationinduced lesions.     

几种基于FFT的频率估计方法精度分析

介绍了噪声背景中正弦信号频率估计的方差下限，对利用FFT主瓣内两条幅度最大谱线进行插值的频率估计方法（Rife-Jane方法和Quinn方法）以及利用FFT相位进行频率插值的方法（分段FFT相位差法和重叠FFT相位差法）的方差进行了理论分析，推导了Quinn方法的频率估计方差计算公式．提出了通过滤波进一步提高分段FFT相位差法的频率估计精度的方法。通过计算机MonteCarlo模拟实验对上述各种方法的频率估计精度以及加窗函数的影响进行了分析并与理论下限进行了比较，指出了每种方法所能达到的估计精度。     

Estimation of the correlation amplitude of RF signals in small cutaneous vessels

Time domain correlation technique is a widely used method for blood flow velocity measurement. The time shift between a pair of windowed ultrasonic echoes is estimated by searching the temporal position of the maximum of the interpolated normalized correlation function. Between two consecutive echoes, the acoustical footprint of a group of scatterers, which are transported with the flow, moves and is deformed. This implies a decreasing of the amplitude of the normalized correlation coefficient. In the case of microcirculation (low flow rate, low SNR), the amplitude of the correlation peak can be used to detect the presence of blood flow and to discriminate false and true detections (reliability index). We have numerically evaluated the statistical performances of the cross-correlation algorithm used as a correlation peak amplitude estimator in severe conditions (short correlation window length, low SNR). These theoretical results have been compared with in vitro experimentation on a 100-/spl mu/m-diameter microcirculatory phantom and with in vivo experimentation on a 180-/spl mu/m-diameter vessel of a human leg carrying erysipelas.     

Visualizing the radial and circumferential strain distribution within vessel phantoms using synthetic-aperture ultrasound elastography

Noninvasive elastography (NIVE) produces elastograms that are difficult to interpret because NIVE visualizes strain in the transducer coordinate system. In this paper, we hypothesized that transforming normal and shear strain elastograms to the vessel coordinate system will produce better strain elastograms. To corroborate this hypothesis, we acquired synthetic-aperture (SA) ultrasound data from simulated and physical vessel phantoms. In both studies, SA echo frames were reconstructed from data acquired with a sparse transducer array. The simulation study was performed with homogeneous and heterogenous phantoms, but in the experimental study we used a modified ultrasound scanner to acquire SA data from homogeneous (n = 1) and heterogeneous (n = 3) vessel phantoms. Axial and lateral displacements were estimated by performing two-dimensional cross-correlation analysis on the beamformed RF echo frames. We generated radial and circumferential strain elastograms by transforming normal and shear strain elastograms to the vessel coordinate system. The results revealed: 1) radial and circumferential strain elastograms acquired from simulated data had a relative root mean squared error on the order of 0.1%; 2) experimentally acquired radial and circumferential strain elastograms had elastographic contrast-to-noise ratio (CNRe) between 10 and 40 dB, and elastographic signal-to-noise ratio (SNRe) between 10 and 35 dB, depending on the number of active transmission elements employed during imaging; 3) radial and circumferential strain elastograms produced with fewer than 8 active transmission elements were inferior to those computed with a greater number of active elements; and 4) plaques were evident in the strain elastograms, except in those obtained with the sparsest transducer array. This study demonstrated that a syntheticaperture ultrasound system could visualize radial and circumferential strain noninvasively.     

Angular strain estimation method for elastography

In the conventional cross-correlation-based strain estimation, there is a trade-off between the interpolation accuracy and the computational requirement. On the other hand, the autocorrelation-based method does not need interpolation, but it cannot estimate the wide range of displacements for elastography. We have developed a new strain estimator, called the angular strain estimation method, which does not need any interpolation and can estimate strain without restricting the range of displacements. The new method estimates strain utilizing complex correlation between correlated ultrasound signals from pre-and post-compression frames. From simulation and experiments, we found that the angular strain estimation method improves the accuracy and strain image quality compared to the conventional strain estimator using cross correlation with interpolation. Furthermore, it is computationally efficient and can be readily incorporated in ultrasound machines for rea -time elastography.     

A deconvolution filter for improvement of time-delay estimation in elastography

In elastography, tissue under investigation is compressed, and the resulting strain is estimated from the gradient of displacement estimates. Therefore, it is important to accurately estimate the displacements (time-delay) for good quality elastograms. A principal source of error in time-delay estimation in elastography is the decorrelation of the echo signal due to tissue compression (decorrelation noise). Temporal stretching of the postcompression signals has been shown to reduce the decorrelation noise at small strains. In this article, we present a deconvolution filter that reduces the decorrelation even further when applied in conjunction with signal stretching. The performance of the proposed filter is evaluated using simulated data.     

A robust correlation receiver for distance estimation

Many methods for distance estimation, such as the ultrasonic pulse-echo method, involve the estimation of a time-of-flight (TOF). In this paper, a signal model is developed that, apart from the TOF, accounts for an unknown, linear frequency dependent distortion as well as for additive noise. We derive a TOF estimator for this model based on the criteria of maximum likelihood. The resulting receiver can be seen as an extension or generalization of the well known cross-correlation, or “matched filter”, estimator described, e.g., by Nilsson. The novel receiver is found to be more robust against unknown pulse shape distortion than the cross-correlation estimator, giving less biased TOF estimates. Also, bias versus noise sensitivity can be controlled by proper model order selection     

High-frame rate, full-view myocardial elastography with automated contour tracking in murine left ventricles in vivo

Myocardial elastography is a novel method for noninvasively assessing regional myocardial function, with the advantages of high resolution and high precision. The purpose in this paper was to isolate the left ventricle from other structures for better displacement and strain visualization. Using a high-resolution (30 MHz) ultrasound system and a retrospective electrocardiogram (ECG)-gating technique, an extremely high frame rate (up to 8 kHz) was previously shown achievable for full-view (12-mm times 12-mm) myocardial elastography in the murine left ventricle. In vivo experiments were performed in anesthetized normal and infarcted mice [one day after left anterior descending (LAD) coronary artery ligation]. Radio frequency (RF) signals of the left ventricle (LV) in the long-axis view and the associated ECG were simultaneously acquired, with the ECG allowing gating of the RF signals. Incremental axial displacement of the myocardium was estimated using a one-dimensional (1-D) cross-correlation function. The cumulative displacement and strain then were calculated from the incremental displacement. In this paper, after manual selection of 40-50 points along the endo-and epicardial borders in the first frame of the cine-loop, myocardial contour was automatically tracked across the entire LV throughout a full cardiac cycle, which correctly determined the region of interest (ROI) for better interpretation. The cine-loop of the cumulative displacement and strain in one cardiac cycle, in both the normal and infarcted cases, showed that motion and deformation in the infarcted myocardium were significantly reduced, and that the infarcted region underwent thinning, rather than thickening, during systole. High precision of the displacement estimation, due to high frequency (30 MHz) and high frame rate (up to 8 kHz) available with this system, allowed for automated tracking of a manually-initialized myocardial contour over an entire cardiac cycle. High frame rate, full-view myocardial elastography with automated contour tracking could provide regional strain information of the LV throughout an entire cardiac cycle, and characterize normal as well as detect abnormal myocardial function, such as an infarction. The method of automated contour tracking can further enhance the capability of the elastographic technique with minimal user intervention while providing accurate functional information for the detection of disease throughout the entire cardiac cycle.     

Doppler spectral estimation using time-frequency distributions

The time-frequency distribution (TFD) of Doppler blood flow signals is usually obtained using the spectrogram, which requires signal stationarity and is known to produce large estimation variance. This paper examines four alternative, nonstationary spectral estimators: a smoothed pseudo-Wigner distribution (SPWD), the Choi-Williams distribution (CWD), the Bessel distribution (BD), and the novel, adaptive constant-Q distribution (AQD) for their applicability to Doppler ultrasound. A synthetic Doppler signal, simulating the nonaxial and pulsatile flow of the common carotid artery, was used for quantitative comparisons at different signal-to-noise-ratios (SNR) of 0, 10, 20, and 30 dB as well as noise free. The cross-correlation (rho) and the root-mean-square-error (RMSE) were calculated after log-compression for each technique and SNR relative to the theoretical distribution. The AQD consistently had the lowest RMSE (/=0.889) of all the TFDs, irrespective of the SNR. The SPWD performed better than the spectrogram, which performed better than the BD and the CWD. Qualitative comparisons were carried out using in vivo data acquired with a 10 MHz ultrasound cuff transducer positioned around the distal aorta of a rabbit. In vivo, the AQD was considered best with respect to background noise and internal gray scale features; it was rated second (after the spectrogram) in depicting the spectral envelope. The AQD performed better as a Doppler spectral estimator than the traditional spectrogram and the other TFDs under the conditions studied here.     

In-vivo imaging of skin under stress: potential of high-frequency (20 MHz) static 2-D elastography

The aim of this study was to evaluate the potential of high-frequency static two-dimensional (2-D) elastography for in vivo exploration of the mechanical behavior of skin. Our device was based on the combination of a 20 MHz sonographer and a patented extensiometer device able to apply calibrated uniaxial stretching of the skin. We used a new algorithm to compute elastograms that improve elastographic signal-to-noise ratio (SNRe) without sacrificing resolution. Mechanical behavior was described according to the axial strain and lateral displacements induced in the tissue. The efficacy of the strain anpolyvinyl alcohol first evaluated in polyvinyl alcohol (PVA)-cryogel phantoms. Several in vivo experiments then were conducted, mainly with the multistretching averaging method, and demonstrated the potential of this technique in the evaluation of mechanical behavior of the dermis and the hypodermis under stress.