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.     

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.     

A fundamental limit on delay estimation using partially correlatedspeckle signals

Delay estimation is used in ultrasonic imaging to estimate blood or soft tissue motion, to measure echo arrival time differences for phase aberration correction, and to estimate displacement for tissue elasticity measurements. In each of these applications delay estimation is performed using speckle signals which are at least partially decorrelated relative to one another. Delay estimates which utilize such data are subject to large errors known as false peaks and smaller magnitude errors known as jitter. While false peaks can sometimes be removed through nonlinear processing, jitter errors place a fundamental limit on the performance of delay estimation techniques. The authors apply the Cramer-Rao Lower Bound to derive an analytical expression which predicts the magnitude of jitter errors incurred when estimating delays using radio frequency (RF) data from speckle targets. The analytical expression presented includes the effects of signal decorrelation due to physical processes, corruption by electronic noise, and a number of other factors. Simulation results are presented which show that the performance of the normalized cross correlation algorithm closely matches theoretical predictions. These results indicate that for poor signal to noise ratios (0 dB) a small improvement in signal to noise ratio can dramatically reduce jitter magnitude. At high signal to noise ratios (30 dB) small amounts of signal decorrelation can significantly increase the magnitude of jitter errors     

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.     

Multiresolution imaging in elastography

The range of strains that can be imaged by any practical elastographic imaging system is inherently limited, and a performance measure is valuable to evaluate these systems from the signal and noise properties of their output images. Such a measure was previously formulated for systems employing cross-correlation based time-delay estimators through the strain filter. While the strain filter predicts the signal-to-noise ratio (SNR(e)) for each tissue strain in the elastogram and provides valuable insights into the nature of image noise, it understated the effects of image resolution (axial resolution, as determined by the cross-correlation window length) on the noise. In this work, the strain filter is modified to study the strain noise at multiple resolutions. The effects of finite window length on signal decorrelation and on the variance of the strain estimator are investigated. Long-duration windows are preferred for improved sensitivity, dynamic range, and SNR(e). However, in this limit the elastogram is degraded due to poor resolution. The results indicate that for nonzero strain, a window length exists at which the variance of strain estimator attains its minima, and consequently the elastographic sensitivity, dynamic range and SNR(e) are strongly affected by the selected window length. Simulation results corroborate the theoretical results, illustrating the presence of a window length where the strain estimation variance is minimized for a given strain value. Multiresolution elastography, where the strain estimate with the highest SNR(e) obtained by processing the pre- and post-compression waveforms at different window lengths is used to generate a composite elastogram and is proposed to improve elastograms. All the objective elastogram parameters (namely: SNR(e), dynamic range, sensitivity and the average elastographic resolution-defined as the cross-correlation window length) are improved with multiresolution elastography when compared to the traditional method of utilizing a single window length to generate the elastogram. Experimental results using a phantom with a hard inclusion illustrates the improvement in elastogram obtained using multiresolution analysis.     

A comparison of the performance of time-delay estimators in medical ultrasound

Time-delay estimation (TDE) is a common operation in ultrasound signal processing. In applications such as blood flow estimation, elastography, phase aberration correction, and many more, the quality of final results is heavily dependent upon the performance of the time-delay estimator implemented. In the past years, several algorithms have been developed and applied in medical ultrasound, sonar, radar, and other fields. In this paper we analyze the performances of the widely used normalized and non-normalized correlations, along with normalized covariance, sum absolute differences (SAD), sum squared differences (SSD), hybrid-sign correlation, polarity-coincidence correlation, and the Meyr-Spies method. These techniques have been applied to simulated ultrasound radio frequency (RF) data under a variety of conditions. We show how parameters, which include center frequency, fractional bandwidth, kernel window size, signal decorrelation, and signal-to-noise ratio (SNR) affect the quality of the delay estimate. Simulation results also are compared with a theoretical performance limit set by the Cramer-Rao lower bound (CRLB). Results show that, for high SNR, high signal correlation, and large kernel size, all of the algorithms closely match the theoretical bound, with relative performances that vary by as much as 20%. As conditions degrade, the performances of various algorithms differ more significantly. For signals with a correlation level of 0.98, SNR of 30 dB, center frequency of 5 MHz with a fractional bandwidth of 0.5, and kernel size of 2 /spl mu/s, the standard deviation of the jitter error is on the order of few nanoseconds. Normalized correlation, normalized covariance, and SSD have an approximately equal jitter error of 2.23 ns (the value predicted by the CRLB is 2.073 ns), whereas the polarity-coincidence correlation performs less well with a jitter error of 2.74 ns.     

Echo decorrelation from displacement gradients in elasticity and velocity estimation

Several ultrasonic techniques for the estimation of blood velocity, tissue motion and elasticity are based on the estimation of displacement through echo time-delay analysis. A common assumption is that tissue displacement is constant within a short observation time used for time delay estimation (TDE). The precision of TDE is mainly limited by noise sources corrupting the echo signals. In addition to electronic and quantization noise, a substantial source of TDE error is the decorrelation of echo signals because of displacement gradients within the observation time. The authors present a theoretical model that describes the mean changes of the crosscorrelation function as a function of observation time and displacement gradient. The gradient is assumed to be small and uniform within the observation time; the decorrelation introduced by the lateral and elevational displacement components is assumed to be small compared with the decorrelation caused by the axial component. The decorrelation model predicts that the expected value of the crosscorrelation function is a low-pass filtered version of the autocorrelation function (i.e., the crosscorrelation obtained without gradients). The filter is a function of the axial gradient and the observation time. This theoretical finding is corroborated experimentally. Limitations imposed by decorrelation in displacement estimation and potential uses of decorrelation in medical ultrasound are discussed.     

Speckle tracking methods for ultrasonic elasticity imaging using short-time correlation

In ultrasound elasticity imaging, strain decorrelation is a major source of error in displacements estimated using correlation techniques. This error can be significantly decreased by reducing the correlation kernel. Additional gains in signal-to-noise ratio (SNR) are possible by filtering the correlation functions prior to displacement estimation. Tradeoffs between spatial resolution and estimate variance are discussed, and estimation in elasticity imaging is compared to traditional time-delay estimation. Simulations and experiments on gel-based phantoms are presented. The results demonstrate that high resolution, high SNR strain estimates can be computed using small correlation kernels (on the order of the autocorrelation width of the ultrasound signal) and correlation filtering.     

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     

Enhancement of echo-signal correlation in elastography using temporal stretching

Echo-signal decorrelation due to tissue compression is a significant source of error in tissue displacement estimates obtained using crosscorrelation. Tissue displacement estimates are used to compute strain values for imaging the elasticity of biological soft tissues. The correlation coefficient between the pre- and post-compression echo rf signals reduces rapidly with signal decorrelation due to increased compression. Miniscule reductions in the value of the correlation coefficient can have a significant impact on the performance of the strain estimator as illustrated by the strain filter. Reducing the rate of signal decorrelation using temporal stretching (which improves the value of the correlation coefficient), significantly improves the performance of the strain filter. The reduction in the rate of signal decorrelation with the subsequent increase in the correlation coefficient using temporal stretching is discussed in this paper. Theoretical, simulation and experimental results quantify the enhancement in the value of the correlation coefficient attained with temporal stretching.     

Filter-based compounded delay estimation with application to strain imaging

Ultrasonic wave interference produces local fluctuations in both the envelope, known as speckle, and phase of echoes. Furthermore, such fluctuations are correlated in space, and subsequent motion estimation from the envelope and/or phase signal produces patterned, correlated errors. Compounding, or combining information from multiple decorrelated looks, reduces such effects. We propose using a filter bank to create multiple looks to produce a compounded motion estimate. In particular, filtering in the lateral direction is shown to preserve delay estimation accuracy in the filtered sub-bands while creating decorrelation between sub-bands at the expense of some lateral resolution. For Gaussian apodization, we explicitly compute the induced signal decorrelation produced by Gabor filters. Furthermore, it is shown that lateral filtering is approximately equivalent to steering, in which filtered sub-bands correspond to signals extracted from shifted sub-apertures. Field II simulation of a point spread function verifies this claim. We use phase zero and its variants as displacement estimators for our compounded result. A simplified deformation model is used to provide computer simulations of deforming an elastic phantom. Simulations demonstrate root mean square error (RMSE) reduction in both displacement and strain of the compounded result over conventional and its laterally blurred versions. Then we apply the methods to experimental data using a commercial elastic phantom, demonstrating an improvement in strain SNR.     

On velocity estimation using speckle decorrelation

Quantitative estimation of blood velocity using Doppler techniques is fundamentally limited because only the axial component can be detected. Speckle decorrelation resulting from scatterer motion may be used to compute non-axial components and to obtain quantitative flow information. Based on both simulations and experimental results, it is shown that the decorrelation technique is feasible only for constant flows. If flow gradients are present, the correlation between two signals along the same line of observation may be significantly affected by the gradients. Therefore, the decorrelation method cannot be used for quantitative flow estimation if flow gradients are not accurately measured and effects on signal correlation are not fully compensated. Results in this paper show that accurate estimation of flow gradients is practically difficult. It is further shown that effects of signal-to-noise ratio (SNR) on the correlation must also be taken into account for quantitative flow analysis.     

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.     

Determination of an optimal image frame interval for frame-to-frame ultrasound image motion tracking

Several important clinical applications depend on accurate ultrasound image frame-to-frame motion estimation. Assuming that there is a degree of finite noise in the image frames and that speckle partially decorrelates between successive frames during freehand scanning, we hypothesize that an optimal inter-frame interval (step size) must exist that provides the smallest relative dimensional error over a set of accumulated motion estimates. Smaller frame increments suffer from less decorrelation-related inaccuracy but present greater potential for cumulative error because more estimates are used over any specific dimensional interval. We studied these effects using a combination of theoretical modeling, numerical simulation, and experiments. Components of diagonal motion due to the limitations of manual transducer movement were considered as the cause of decorrelation. The results were examined for four different angles of the diagonal motion and two different signal-to-noise ratio (SNR) values. These indicate that an optimal step size does exist and that this is dependent on many variables including SNR, angle of the diagonal motion, transducer geometry, lens focusing parameters, transducer operating frequency, and beamforming parameters. In practical experiments, we found that the optimal step size generally required using every available image frame rather than 'skipping' any intermediate frames.     

Frequency-domain-based strain estimation and high-frame-rate imaging for quasi-static elastography

In freehand elastography, quasi-static tissue compression is applied through the ultrasound probe, and the corresponding axial strain is estimated by calculating the time shift between consecutive echo signals. This calculation typically suffers from a poor signal-to-noise ratio or from the decorrelation between consecutive echoes resulting from an erroneous axial motion impressed by the operator. This paper shows that the quality of elastograms can be improved through the integration of two distinct techniques in the strain estimation procedure. The first technique evaluates the displacement of the tissue by analyzing the phases of the echo signal spectra acquired during compression. The second technique increases the displacement estimation robustness by averaging multiple displacement estimations in a high-frame-rate imaging system, while maintaining the typical elastogram frame-rate. The experimental results, obtained with the Ultrasound Advanced Open Platform (ULA-OP) and a cyst phantom, demonstrate that each of the proposed methods can independently improve the quality of elastograms, and that further improvements are possible through their combination.     

A successive parameter estimation algorithm for chirplet signal decomposition

In ultrasonic imaging systems, the patterns of detected echoes correspond to the shape, size, and orientation of the reflectors and the physical properties of the propagation path. However, these echoes often are overlapped due to closely spaced reflectors and/or microstructure scattering. The decomposition of these echoes is a major and challenging problem. Therefore, signal modeling and parameter estimation of the nonstationary ultrasonic echoes is critical for image analysis, target detection, and object recognition. In this paper, a successive parameter estimation algorithm based on the chirplet transform is presented. The chirplet transform is used not only as a means for time-frequency representation, but also to estimate the echo parameters, including the amplitude, time-of-arrival, center frequency, bandwidth, phase, and chirp rate. Furthermore, noise performance analysis using the Cramer Rao lower bounds demonstrates that the parameter estimator based on the chirplet transform is a minimum variance and unbiased estimator for signal-to-noise ratio (SNR) as low as 2.5 dB. To demonstrate the superior time-frequency and parameter estimation performance of the chirplet decomposition, ultrasonic flaw echoes embedded in grain scattering, and multiple interfering chirplets emitted by a large, brown bat have been analyzed. It has been shown that the chirplet signal decomposition algorithm performs robustly, yields accurate echo estimation, and results in SNR enhancements. Numerical and analytical results show that the algorithm is efficient and successful in high-fidelity signal representation.     

A time-efficient and accurate strain estimation concept for ultrasonic elastography using iterative phase zero estimation

In ultrasonic elastography, the exact estimation of temporal displacements between two signals is the key to estimating strain. An algorithm was previously proposed that estimates these displacements using phase differences of the corresponding base-band signals. A major advantage of these algorithms compared with correlation techniques is the computational efficiency. In this paper, an extension of the algorithm is presented that iteratively takes into account the time shifts of the signals to overcome the problems of aliasing and accuracy in the estimation of the phase shift. Thus, it can be proven that the algorithm is equivalent to the search of the maximum of the correlation function. Furthermore, a robust logarithmic compression is proposed that only compresses the envelope of the signal. This compression does not introduce systematic errors and significantly reduces decorrelation noise. The resulting algorithm is a computationally simple and very fast alternative to conventional correlation techniques, and the accuracy of strain images is improved.     

Correlation analysis for angular compounding in strain imaging

Spatial angular compounding for elastography is a new technique that enables the reduction of noise artifacts in elastograms. This technique is most effective when the angular strain estimates to be averaged or compounded are uncorrelated. In this paper, we present a theoretical analysis of the correlation between pre- and postcompression radio-frequency echo signals acquired from the same location but at different beam insonification angles. The accuracy of the theoretical results is verified using radiofrequency pre- and postcompression echo signals acquired using a real-time clinical scanner on tissue-mimicking uniformly elastic and homogenous phantoms. The theory predicts an increased signal decorrelation with an increase in the beam-steered insonification angle as the applied strain increases and for increasing depths in the medium. Theoretical results provide useful information regarding the correlation of the angular strain estimates obtained from different beam angles that helps in finding optimum compounding schemes for elastography.     

Improving IVUS palpography by incorporation of motion compensation based on block matching and optical flow

Intravascular ultrasound (IVUS) strain imaging of the luminal layer in coronary arteries, coined as IVUS palpography, utilizes conventional radio frequency (RF) signals acquired at 2 different levels of a compressional load. The signals are cross-correlated to obtain the microscopic tissue displacements, which can be directly translated into local strain of the vessel wall. However, (apparent) tissue motion and nonuniform deformation of the vessel wall, due to catheter wiggling, reduce signal correlation and result in invalid strain estimates. Implications of probe motion were studied on the tissue-mimicking phantom. The measured circumferential tissue displacement and level of the speckle decorrelation amounted to 12° and 0.58, respectively, for the catheter displacement of 456 μm. To compensate for the motion artifacts in IVUS palpography, a novel method based on the feature-based scale-space optical flow (OF), and classical block matching (BM) algorithm, were employed. The computed OF vector and BM displacement fields quantify the amount of local tissue misalignment in consecutive frames. Subsequently, the extracted circumferential displacements are used to realign the signals before strain computation. Motion compensation reduces the RF signal decorrelation and increases the number of valid strain estimates. The advantage of applying the motion correction in IVUS palpography was demonstrated in a midscale validation study on 14 in vivo pullbacks. Both methods substantially increase the number of valid strain estimates in the partial and compounded palpograms. Mean relative improvement in the number of valid strain estimates with motion compensation in comparison to one without motion compensation amounts to 28% and 14%, respectively. Implementation of motion compensation methods boosts the diagnostic value of IVUS palpography.     

2-D companding for noise reduction in strain imaging

Companding is a signal preprocessing technique for improving the precision of correlation-based time delay measurements. In strain imaging, companding is applied to warp 2-D or 3-D ultrasonic echo fields to improve coherence between data acquired before and after compression. It minimizes decorrelation errors, which are the dominant source of strain image noise. The word refers to a spatially variable signal scaling that compresses and expands waveforms acquired in an ultrasonic scan plane or volume. Temporal stretching by the applied strain is a single-scale (global), 1-D companding process that has been used successfully to reduce strain noise. This paper describes a two-scale (global and local), 2-D companding technique that is based on a sum-absolute-difference (SAD) algorithm for blood velocity estimation. Several experiments are presented that demonstrate improvements in target visibility for strain imaging. The results show that, if tissue motion can be confined to the scan plane of a linear array transducer, displacement variance can be reduced two orders of magnitude using 2-D local companding relative to temporal stretching.