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.     

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.     

Phase rotation methods in filtering correlation coefficients for ultrasound speckle tracking

In speckle-tracking-based myocardial strain imaging, large interframe/volume peak-systolic strains cause peak hopping artifacts separating the highest correlation coefficient peak from the true peak. A correlation coefficient filter was previously designed to minimize peak hopping artifacts. For large strains, however, the correlation coefficient filter must follow the strain distribution to remove peak hopping effectively. This processing usually means interpolation and high computational load. To reduce the computational burden, a narrow band approximation using phase rotation is developed in this paper to facilitate correlation coefficient filtering. Correlation coefficients are first phase rotated to increase coherence, then filtered. Rotated phase angles are determined by the local strain and spatial position. This form of correlation coefficient filtering enhances true correlation coefficient peaks in large strain applications if decorrelation due to deformation does not completely destroy the coherence among neighboring correlation coefficients. The assumed strain used in the filter can also deviate from the true strain and still be effective. Further improvement in displacement estimation can be expected by combining correlation coefficient filtering with a new Viterbi-based displacement estimator.     

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.     

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.     

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.     

Characterization of Frequency Stability: Effect of RF Filtering

This paper shows that the RF filtering of a signal generated by an oscillator affects the characterization of the frequency stability in a manner that differs from the filtering of the phase of this signal. The effect on both the frequency domain and the time domain measurement is considered. It is shown that the spectral density of the phase fluctuations of the filtered signal is a function of the spectral densities of the amplitude fluctuations and of the phase fluctuations of the original signal. The corresponding expression for the two-sample variance (Allan variance) is then also a function of these two contributions. Detailed calculation is made for the case of a signal with frequency stability limited by white phase noise and filtered by a first-order, low-pass filter. It is found that the frequency stability is improved by more filtering if the cutoff frequency, fc, is higher than the signal frequency, f0, as is the case for phase filtering. However, the stability will degrade with more filtering if fc < f0. An optimum frequency stability is reached when fc = f0/?2. Experimental measurements confirm these theoretical predictions.     

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     

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.     

Strain compounding: a new approach for speckle reduction

A new compounding technique for reducing speckle brightness variations is proposed. This method exploits the decorrelation between signals under different strain states. The different strain states can be created using externally applied forces such as the ones used in sonoelastography. Such forces produce three-dimensional tissue motion. By correcting only the in-plane (i.e., axial and lateral) motion, the images under different strain states have similar characteristics except for speckle appearance caused by the uncorrected out-of-plane (i.e., elevational) motion. Additional speckle decorrelation is also introduced through tissue motion correction caused by the change of effective in-plane sample volume geometry. Therefore, these images can be combined for speckle reduction with less degradation in in-plane spatial resolution than conventional approaches. In this paper, three-dimensional tissue motion under various strain conditions were simulated. It was found that significant speckle decorrelation existed at strains achievable in some clinical situations. Experiments were also conducted to test efficacy of this approach. Pulse-echo data from a gelatin-based phantom were acquired using a 5-MHz, single crystal transducer, and both conventional and compound B-mode images were formed. Results indicated that speckle brightness variations were reduced, and detectability of low contrast objects was enhanced. Performance limitations and fundamental differences between the proposed technique and existing techniques are discussed     

Speckle-motion artifact under tissue shearing

Research has shown that, for a rotating phantom, the speckle pattern may not replicate the phantom motion, rather it may show a large lateral translation component in addition to rotation. This translation effect was labeled speckle-motion artifact. An image formation model has been shown to explain the phenomenon, pointing to the curvature of the imaging system point spread function (PSF) at the origin of this effect. The present paper extends this analysis and proposes a model, which predicts that a lateral motion artifact also would occur with shear motion. In the model, the artifact is found to be proportional to the shear angle and dependent of shear orientation, being maximal for shear that runs parallel to the axial direction; as for rotation, the artifact increases with frequency and beamwidth. This would mean that, when viewing a parabolic flow in the far field or with a highly curved PSF, an apparent contraction/expansion pattern in the direction of the vessel wall would be superimposed to the real velocity profile. In elastography, when viewing an inclusion subjected to an axial strain, four motion artifact regions are expected near the inclusion. The model is developed using the Fourier domain representation of the speckles for tissue-motion compensated signals, also called Lagrangian speckle. It can explain the artifact in terms of a simple spectral translation of a parabolic phase profile; given this, it is shown the artifact would be proportional to the lateral derivative of the axial displacement field. The spectral representation of Lagrangian speckle, for shear, also provides a simple geometrical interpretation for speckle decorrelation in terms of the shear strength and orientation, and in terms of the beam characteristics, i.e., the axial and lateral bandwidth.     

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.     

Estimates of echo correlation and measurement bias in acoustic radiation force impulse imaging

Acoustic radiation force impulse (ARFI) imaging is a novel imaging modality in which pulses from a diagnostic ultrasound scanner are used to displace tissue and track its motion. The region displaced has lateral and elevational dimensions of similar scale to the ultrasound beams used to track the motion. Therefore, there is a range of tissue displacements present within the tracking beam, leading to decorrelation of the echo signal. Expressions are derived for the expected value of the displacement estimate and the cross-correlation at the expected displacement. Numerical simulations confirm the analytical model.     

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.     

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.     

Acoustic attenuation estimation for soft tissue from ultrasound echo envelope peaks

A theoretical framework of a modified EP (envelope peak) method is developed. In this method, a wideband echo signal from each A line (one echo sequence) is first filtered in parallel by a bank of narrow-bandpass filters using a split-spectrum processing. The attenuation is then estimated from the EPs of each filtered signal using a narrowband technique. The combination of the split-spectrum processing with the narrowband technique enables the accuracy of the attenuation estimation to be well controlled without the precise measurements of the spectral shape and parameters of the transmitted pulses. On the other hand, the precision of the estimation is still determined by the bandwidth of the original echo signal, and is not affected by the split-spectrum processing. As a result, the modified EP method improves the accuracy of the attenuation estimation while retaining the high precision of the original EP method. Results from phantom experiments supported the theoretical analysis.     

PSF dedicated to estimation of displacement vectors for tissue elasticity imaging with ultrasound

This paper investigates a new approach devoted to displacement vector estimation in ultrasound imaging. The main idea is to adapt the image formation to a given displacement estimation method to increase the precision of the estimation. The displacement is identified as the zero crossing of the phase of the complex cross-correlation between signals extracted from the lateral direction of the ultrasound RF image. For precise displacement estimation, a linearity of the phase slope is needed as well as a high phase slope. Consequently, a particular point spread function (PSF) dedicated to this estimator is designed. This PSF, showing oscillations in the lateral direction, leads to synthesis of lateral RF signals. The estimation is included in a 2-D displacement vector estimation method. The improvement of this approach is evaluated quantitatively by simulation studies. A comparison with a speckle tracking technique is also presented. The lateral oscillations improve both the speckle tracking estimation and our 2-D estimation method. Using our dedicated images, the precision of the estimation is improved by reducing the standard deviation of the lateral displacement error by a factor of 2 for speckle tracking and more than 3 with our method compared to using conventional images. Our method performs 7 times better than speckle tracking. Experimentally, the improvement in the case of a pure lateral translation reaches a factor of 7. Finally, the experimental feasibility of the 2-D displacement vector estimation is demonstrated on data acquired from a Cryogel phantom.