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.     

Image restoration with the Viterbi algorithm

The Viterbi algorithm (VA) is known to given an optimal solution to the problem of estimating one-dimensional sequences of discrete-valued pixels corrupted by finite-support blur and memoryless noise. A row-by-row estimation along with decision feedback and vector quantization is used to reduce the computational complexity of the VA and allow the estimation of two-dimensional images. This reduced-complexity VA (RCVA) is shown to produce near-optimal estimation of random binary images. In addition, simulated restorations of gray-scale images show the RCVA estimates to be an improvement over the estimates obtained by the conventional Wiener filter (WF). Unlike the WF, the RCVA is capable of superresolution and is adaptable for use in restoring data from signal-dependent Poisson noise corruption. Experimental restorations of random binary data gathered from an optical imaging system support the simulations and show that the RCVA estimate has fewer than one third of the errors of the WF estimate.     

Temperature estimation using ultrasonic spatial compound imaging

The feasibility of temperature estimation during high-intensity focused ultrasound therapy using pulse-echo diagnostic ultrasound data has been demonstrated. This method is based upon the measurement of thermally-induced modifications in backscattered RF echoes due to thermal expansion and local changes in the speed of sound. It has been shown that strong ripple artifacts due to the thermo-acoustic lens effect severely corrupt the temperature estimates behind the heated region. We propose here a new imaging technique that improves the temperature estimation behind the heated region and reduces the variance of the temperature estimates in the entire image. We replaced the conventional beamforming on transmit with multiple steered plane wave insonifications using several subapertures. A two-dimensional temperature map is estimated from axial displacement maps between consecutive RF images of identically steered plane wave insonifications. Temperature estimation is then improved by averaging the two-dimensional maps from the multiple steered plane wave insonifications. Experiments were conducted in a tissue-mimicking gelatin-based phantom and in fresh bovine liver.     

Porosity estimation using the frequency dependence of the ultrasonic attenuation

A new technique is reported for estimating the volume fraction of porosity in structural materials. The estimate for the volume fraction is proportional to the slope of the ultrasonic attenuation when plotted as a function of frequency. Both theory and experiment are considered. The theory, appropriate for dilute porosity, uses the uncorrelated, single-scatter approximation. An attenuation slope algorithm is derived within this approximation and its limits of validity are tested by computer simulation. Experimental tests consist of three parts. First, the method is compared with other existing techniques through estimates from the published data on gas porosity in aluminum casts. For the second test, cylindrical porosity is simulated by parallel through-holes drilled in aluminum blocks. Finally, the attenuation in porous graphite-epoxy samples is measured and compared with results predicted from theory.     

Internal displacement and strain imaging using ultrasonic speckletracking

Previous ultrasound speckle tracking methods have been extended, permitting measurement of internal displacement and strain fields over a wide dynamic range of tissue motion. The markedly increased dynamic range of this approach should lead to enhanced contrast resolution in strain and elasticity images. Results of experiments on gelatin-based, tissue equivalent phantoms show the capabilities of the method     

C- and D-weighted ultrasonic imaging using the translating apertures algorithm

Conventional ultrasonic imaging systems depict tissue backscatter, that is, the ultrasonic energy reflected directly back toward the transmitter. Although diagnostically useful, these systems fail to exploit the information available in components of the sound field scattered in other directions. This paper describes a new method of imaging this angular scatter. First, the translating apertures algorithm (TAA) is used to acquire data at two scattering angles. Then, these data are processed to yield an image of the common scattering with angle and the differential scattering with angle. This paper explores the potential of these common-weighted (c-weighted) and difference-weighted (d-weighted) images using theory and simulations. In addition, it describes and analyzes the performance of the TAA when it is applied using multiple receive elements. Analysis is presented that shows that, in Rayleigh scattering environments, c- and d-weighted images depict compressibility and density variations, respectively. A simulated image and accompanying analysis are presented that show the potential of these techniques to improve soft tissue contrast and to increase the detectability of microcalcifications. A comparison with previous angular scatter measurement techniques shows that use of the TAA significantly reduces statistical variability in measured angular scatter profiles. Spatially localized, statistically reliable angular scatter measurements will enable a broad range of angular scatter imaging techniques. C- and d-weighted imaging may ultimately he applied clinically to identify calcification in atherosclerotic plaques and breast tumors     

The wavenumber algorithm for full-matrix imaging using an ultrasonic array

Ultrasonic imaging using full-matrix capture, e.g., via the total focusing method (TFM), has been shown to increase angular inspection coverage and improve sensitivity to small defects in nondestructive evaluation. In this paper, we develop a Fourier-domain approach to full-matrix imaging based on the wavenumber algorithm used in synthetic aperture radar and sonar. The extension to the wavenumber algorithm for full-matrix data is described and the performance of the new algorithm compared with the TFM, which we use as a representative benchmark for the time-domain algorithms. The wavenumber algorithm provides a mathematically rigorous solution to the inverse problem for the assumed forward wave propagation model, whereas the TFM employs heuristic delay-and-sum beamforming. Consequently, the wavenumber algorithm has an improved point-spread function and provides better imagery. However, the major advantage of the wavenumber algorithm is its superior computational performance. For large arrays and images, the wavenumber algorithm is several orders of magnitude faster than the TFM. On the other hand, the key advantage of the TFM is its flexibility. The wavenumber algorithm requires a regularly sampled linear array, while the TFM can handle arbitrary imaging geometries. The TFM and the wavenumber algorithm are compared using simulated and experimental data.     

Flaw signature estimation in ultrasonic nondestructive evaluation using the Wiener filter with limited prior information

Flaw signals measured in ultrasonic testing include the effects of the measurements system and are corrupted by noise. The measurement system response is both bandlimited and frequency dependent within the bandwidth, resulting in measured signals which are blurred and distorted estimates of actual flaw signatures. The Wiener filter can be used to estimate the flaw's scattering amplitude by removing the effect of the measurement system in the presence of noise. A method is presented for implementing an optimal form of the Wiener filter that requires only estimates of the noise distribution parameters. The theoretical error for scattering amplitude estimation, assuming various levels of available prior information, is analyzed. Three estimation techniques, one a maximum-likelihood based method and the other two residual-sum-of-squares methods, are formulated and tested. The results demonstrate that any of the three approaches could be used to optimally implement the alternative form of the Wiener filter with limited prior information.     

Adaptive strain estimation using retrospective processing [medical US elasticity imaging

Because errors in displacement and strain estimates depend on the magnitude of the induced strain, the strain signal-to-noise ratio (SNR) will be a function of the applied deformation. If deformation is applied at the body surface, it is difficult during data acquisition to select a single surface displacement providing the highest strain SNR throughout the image. By applying continuous deformation and capturing data in real-time, the surface displacement providing the highest strain SNR can be selected retrospectively. A method to adaptively optimize strain SNR over the image plane using retrospective processing is presented and demonstrated with experimental results.     

The energy demand estimation for Turkey using differential evolution algorithm

The energy demand estimation commands great importance for both developing and developed countries in terms of the economy and country resources. In this study, the differential evolution algorithm (DE) was used to forecast the long-term energy demand in Turkey. In addition to being employed for solving regular optimization problems, DE is also a global, meta-heuristic algorithm that enables fast, reliable and operative stochastic searches based on population. Considering the correlation between the increase in certain economic indicators in Turkey and the increase of energy consumption, two equations were used—one applying the linear form and the other the quadratic form. Turkey’s long-term energy demand from 2012 to 2031 was estimated through the DE method in three different scenarios and in terms of the gross domestic product, import, export and population. To prove the success of the DE method in addressing the energy demand problem, the DE method was compared to other methods found in the literature. Results showed that the proposed DE method was more successful than the other methods. Furthermore, the future projections of energy demand obtained using the proposed method were compared to the indicators of energy demand estimated and observed by the Ministry of Energy and Natural Resources.     

Parameter estimation of the intensity process of self-excitingpoint processes using the EM algorithm

This paper presents a method of estimating the parameters of intensity processes in the self-exciting point process (SEPP) with the expectation-maximization (EM) algorithm. In the present paper, the case is considered where the intensity process of SEPPs is dependent only on the latest occurrence, i.e., one-memory SEPPs, as well as where the impulse response function characterizing the intensity process is parameterized as a single exponential function having a constant coefficient that takes a positive or negative value, i.e., making it possible to model a self “-exciting” or “-inhibiting” point process. Then, an explicit formula is derived for estimating the parameters specifying the intensity process on the basis of the EM algorithm, which in this instance gives the maximum likelihood (ML) estimates without solving nonlinear optimization problems. In practical computations, the parameters of interest can be estimated from the histogram of time intervals between point events. Monte Carlo simulations illustrate the validity of the derived estimation formulas and procedures     

A spline-based algorithm for continuous time-delay estimation using sampled data

Time delay estimation (TDE) lies at the heart of signal processing algorithms in a broad range of application areas, including communications, coherent imaging, speech processing, and acoustics. In medical ultrasound for example, TDE is used in blood flow estimation, tissue motion measurement, tissue elasticity estimation, phase aberration correction, and a number of other algorithms. Because of its central significance, TDE accuracy, precision, and computational cost are of critical importance. Furthermore, because TDE is typically performed on sampled signals-and delay estimates are usually desired over a continuous domain-time delay estimator performance should be considered in conjunction with associated interpolation. In this paper we present a new time-delay estimator that directly determines continuous time-delay estimates from sampled data. The technique forms a spline-based, piecewise continuous representation of the reference signal then solves for the minimum of the sum squared error between the reference and the delayed signals to determine their relative time delay. Computer simulation results clearly show that the proposed algorithm significantly outperforms other algorithms in terms of jitter and bias over a broad range of conditions. We also describe a modified version of the algorithm that includes companding with only a minor increase in computational cost.     

Tissue strain imaging using a wavelet transform-based peak search algorithm

A new method is proposed to estimate the motion and relative local compression between two successive ultrasound RF signals under different compression states. The algorithm uses the continuous wavelet transform to locate the peaks in the RF signals. The estimated peaks in the pre- and post-compression signals are assigned to each other by a peak matching technique with the goal of minimizing the number of false matches. The method allows local shifts of the tissue to be estimated. The method has been tested in one-dimensional simulations and phantom experiments. The signal-to-noise ratio and the rms error are shown to be better than for the standard cross-correlation method (CC). The new estimator remains unbiased for up to 10% strain which is a larger range than that of CC. The maximum signal-to-noise ratio is 3 times as high as that of the CC method, showing higher sensitivity as well. The method is computationally efficient, achieving 0.7 msec/RF line on a standard personal computer.     

修正倒谱和动态规划的基频估计算法

基音频率是语音信号处理中的一个重要参数。倍频、半频错误以及清浊音判决的可靠性等问题一直是基频估计中的难点问题。在对语音信号的倒谱进行适当修正的基础上,提出了一种高精度的基频估计算法。该算法根据倒谱、短时能量和短时过零率在清音段和浊音段的不同表现,构造了一个清浊音判决函数,大大提高了清浊音判决精度;然后利用动态规划技术进行基频跟踪。在构造代价函数时．充分考虑了基频连续性的影响,从而使该算法既能有效地避免倍频和半频错误,又能体现出基频的自然加倍和减半。通过与现有的几种效果较好的方法进行对比实验,结果表明该算法具有准确率高、基频轨迹平滑的优点,利用该算法得到的基频轨迹基本不需要进行后期平滑处理。     

Least-squares estimation of imaging parameters for an ultrasonic array using known geometric image features

Ultrasonic array images are adversely affected by errors in the assumed or measured imaging parameters. For non-destructive testing and evaluation, this can result in reduced defect detection and characterization performance. In this paper, an autofocus algorithm is presented for estimating and correcting imaging parameter errors using the collected echo data and a priori knowledge of the image geometry. Focusing is achieved by isolating a known geometric feature in the collected data and then performing a weighted leastsquares minimization of the errors between the data and a feature model, with respect to the unknown parameters. The autofocus algorithm is described for the estimation of element positions in a flexible array coupled to a specimen with an unknown surface profile. Experimental results are shown using a prototype flexible array and it is demonstrated that (for an isolated feature and a well-prescribed feature model) the algorithm is capable of generating autofocused images that are comparable in quality to benchmark images generated using accurately known imaging parameters.     

Correlating the plastic strain ratio with ultrasonic velocities in textured metals

A method for predicting the anisotropy of the plastic strain ratio from measurements of ultrasonic velocities is proposed. The calculations are based on the assumption that both the plastic strain ratio and the ultrasonic velocities display the statistical symmetries of the crystal orientation distribution function (ODF). The proposed formula is based on a theoretical calculation of the anisotropy of theR value and the ultrasonic velocities for 28 different textures.     

Two-dimensional ultrasonic strain rate measurement of the human heart in vivo

A study is presented in which the feasibility of two-dimensional strain rate estimation of the human heart in vivo has been demonstrated. To do this, ultrasonic B-mode data were captured at a high temporal resolution of 3.8 ms and processed off-line. The motion of the RF signal patterns within the two-dimensional sector image was tracked and used as the basis for strain rate estimation. Both axial and lateral motion and strain rate estimates showed a good agreement with the results obtained by more established, one-dimensional techniques     

Direct and gradient-based average strain estimation by using weighted nearest neighbor cross-correlation peaks

In this paper, two novel approaches, gradientbased and direct strain estimation techniques, are proposed for high-quality average strain imaging incorporating a cost function maximization. Stiffness typically is a continuous function. Consequently, stiffness of proximal tissues is very close to that of the tissue corresponding to a given data window. Hence, a cost function is defined from exponentially weighted neighboring pre- and post-compression RF echo normalized cross-correlation peaks in the lateral (for displacement estimation) or in both the axial and the lateral (for direct strain estimation) directions. This enforces a controlled continuity in displacement/strain and average displacement/strain is calculated from the corresponding maximized cost function. Axial stress causes lateral shift in the tissue. Therefore, a 1-D post-compression echo segment is selected by incorporating Poisson's ratio. Two stretching factors are considered simultaneously in gradient-based strain estimation that allow imaging the lesions properly. The proposed time-domain gradient-based and direct-strain-estimation-based algorithms demonstrate significantly better performance in terms of elastographic signal-to-noise ratio (SNRe), elastographic contrast-to-noise ratio (CNRe), peak signal-to-noise ratio (PSNR), and mean structural similarity (MSSIM) than the other reported time-domain gradientbased and direct-strain-estimation techniques in finite element modeling (FEM) simulation and phantom experiments. For example, in FEM simulation, it has been found that the proposed direct strain estimation method can improve up to approximately 2.49 to 8.71, 2.2 to 6.63, 1.5 to 5, and 1.59 to 2.45 dB in the SNRe, CNRe, PSNR, and MSSIM compared with the traditional direct strain estimation method, respectively, and the proposed gradient-based algorithm demonstrates 2.99 to 16.26, 18.74 to 23.88, 3 to 9.5, and 0.6 to 5.36 dB improvement in the SNRe, CNRe, PSNR, and MSSIM, respectively, compared with a recently reported time-domain gradient-based technique. The range of improvement as noted above is for low to high applied strains. In addition, the comparative results using the in vivo breast data (including malignant or benign masses) also show that the lesion size is better defined by the proposed gradient-based average strain estimation technique.