A 2D strain estimator with numerical optimization method for soft-tissue elastography

Elastography is a bioelasticity-based imaging modality which has been proved to be a potential evaluation tool to detect the tissue abnormalities. Conventional method for elastography is to estimate the displacement based on cross-correlation technique firstly, then strain profile is calculated as the gradient of the displacement. The main problem of this method arises from the fact that the cross-correlation between pre- and post-compression signals will be decreased because of the signal’s compression-to-deformation. It may constrain the estimation of the displacement. Numerical optimization, as an efficient tool to estimate the non-rigid deformation in image registration, has its potential to achieve the elastogram. This paper incorporates the idea of image registration into elastography and proposes a radio frenquency (RF) signal registration strain estimator based on the minimization of a cost function using numerical optimization method with Powell algorithm (NOMPA). To evaluate the proposed scheme, the simulation data with a hard inclusion embedded in the homogeneous background is produced for analysis. NOMPA can obtain the displacement profiles and strain profiles simultaneously. When compared with the cross-correlation based method, NOMPA presents better signal-to-noise ratio (SNR, 32.6 ± 1.5 dB vs. 23.8 ± 1.1 dB) and contrast-to-noise ratio (CNR, 28.8 ± 1.8 dB vs. 21.7 ± 0.9 dB) in axial normal strain estimation. The in vitro experiment of porcine liver with ethanol-induced lesion is also studied. The statistic results of SNR and CNR indicate that strain profiles by NOMPA performs better anti-noise and target detectability than that by cross-correlation based method. Though NOMPA carry a heavier computational burden than cross-correlation based method, it may be an useful method to obtain 2D strains in elastography.     

The combined effect of nonlinear filtration and window size on the accuracy of tissue displacement estimation using detected echo signals

In cardiac elastography, the regional strain and strain rate imaging is based on displacement estimation of tissue sections within the heart muscle carried out with various block-matching techniques (cross-correlation, sum of absolute differences, sum of squared differences, etc.). The accuracy of these techniques depends on a combination of ultrasonic imaging parameters such as ultrasonic frequency of interrogation, signal-to-noise ratio, size of a kernel used in a block-matching algorithm, type of data and speckle decorrelation. In this paper, we discuss the possibility to enhance the accuracy of the displacement estimation via nonlinear filtering of B-mode images before block-matching operation. The combined effect of a filter algorithm and a kernel size on the accuracy of the displacement estimation is analyzed using a 36-frame sequence of grayscale B-mode images of a human heart acquired by an ultrasound system operating at 1.77 MHz. It is shown that the nonlinear filtering of images enables to obtain the desired accuracy (less than one pixel) of the displacement estimation with smaller kernels than without filtering. These results are obtained for two filters--an adaptive anisotropic diffusion filter and a nonlinear Gaussian filter chain.     

Differential ultrasonic imaging for the characterization of lesions induced by high intensity focused ultrasound

High intensity focused ultrasound (HIFU) is an effective technique for noninvasive local creating coagulative necrotic lesions in deep target volumes without damage to the overlaying or surrounding tissues. It is very important to detect and evaluate lesions generated by HIFU during treatment procedures. This study describes the development of several differential ultrasonic imaging techniques to characterize lesions based on estimation of relative changes in tissue properties derived from backscattered RF data. A single, spherical HIFU transducer was used to produce lesions in soft tissues. The RF signals were recorded as outputs from a modified diagnostic ultrasound system. After some preprocessing, the integrated backscatter values, which can be used as an indicator of the microstructure and backscattering property of tissues, were calculated before and after HIFU treatment. The differential integrated backscatter values were subsequently used to form images revealing the lesion areas. The differential attenuation imaging with the same RF data was also performed, which has been proposed by a few researchers. The results of the differential integrated backscatter imaging were compared with that of the differential attenuation imaging and the former method offers some advantages over the latter method. The two methods above are both based on spectrum analysis and would spend much computational time. Therefore, some simple digital differential imaging methods, including absolute difference (AD), sum absolute differences (SAD), and sum squared differences (SSD) algorithms, were also proposed to detect HIFU-induced lesions. However, these methods cannot provide the information of the degree of tissue damage. Experiments in vitro bovine muscle and liver validated the method of differential integrated backscatter imaging for the characterization of HIFU-induced lesions. And the AD, SAD, and SSD algorithms can be implemented in real-time during HIFU therapy to visualize the lesions.     

Lesion edge preserved direct average strain estimation for ultrasound elasticity imaging

Elasticity imaging techniques with built-in or regularization-based smoothing feature for ensuring strain continuity are not intelligent enough to prevent distortion or lesion edge blurring while smoothing. This paper proposes a novel approach with built-in lesion edge preservation technique for high quality direct average strain imaging. An edge detection scheme, typically used in diffusion filtering is modified here for lesion edge detection. Based on the extracted edge information, lesion edges are preserved by modifying the strain determining cost function in the direct-average-strain-estimation (DASE) method. The proposed algorithm demonstrates approximately 3.42–4.25 dB improvement in terms of edge-mean-square-error (EMSE) than the other reported regularized or average strain estimation techniques in finite-element-modeling (FEM) simulation with almost no sacrifice in elastographic-signal-to-noise-ratio (SNRe) and elastographic-contrast-to-noise-ratio (CNRe) metrics. The efficacy of the proposed algorithm is also tested for the experimental phantom data and in vivo breast data. The results reveal that the proposed method can generate a high quality strain image delineating the lesion edge more clearly than the other reported strain estimation techniques that have been designed to ensure strain continuity. The computational cost, however, is little higher for the proposed method than the simpler DASE and considerably higher than that of the 2D analytic minimization (AM2D) method.     

水声正交频分多址上行通信稀疏信道估计与导频优化

针对水声正交频分多址(OFDMA)上行通信中用户导频数量少、分布不均匀, 导致传统内插信道估计方法产生误码平层的问题, 提出一种稀疏信道估计与导频优化方法. 基于压缩感知(CS)理论估计稀疏信道冲激响应, 并依据CS理论中测量矩阵互相关最小化原理, 提出基于随机搜索的导频图案和导频功率联合优化算法. 仿真结果表明, 所提方法在不同多径扩展信道下的性能均优于基于线性内插的最小二乘估计、未经导频优化的CS信道估计以及单纯基于导频图案优化的CS信道估计. 水池实验分别验证了交织式和广义式子载波分配的水声OFDMA上行通信性能, 在接收信噪比高于10 dB时利用所提方法实现了两用户接入的可靠通信.     

A two-step optical flow method for strain estimation in elastography: Simulation and phantom study

Optical flow (OF) method has been used in ultrasound elastography to estimate the strain distribution in tissues. However the bias of strain estimation by OF has previously been shown to be close to 20%. The objective in this paper is to improve the performance of OF-based strain estimation, a two-step OF method with a local warping technique is proposed in this paper. The local warping technique effectively decreases the decorrelation of the signals, and hence improves the performance of strain estimation. Simulations on both homogeneous and heterogeneous models with different strains are performed. Experiments on a heterogeneous tissue-mimicking phantom are also carried out. Simulation results of the homogeneous model show that the two-step OF method reduces the bias of strain estimation from 23.77% to 1.65%, and reduces the standard deviation of strain estimation from 2.9 × 10⁻³ to 0.47 × 10⁻³. Simulation results of the heterogeneous model shows that the signals-to-noise ratio (SNR_e) of strain estimation is improved by 2.1 and 5.3 dB in the inclusion and background, respectively, and the contrast-to-noise ratio (CNR_e) is improved by 6.8 dB. Finally, results of phantom experiments show that, by using the proposed method, the SNR_e is increased by 4.0 dB and 8.9 dB in the inclusion and background, respectively, while the CNR_e is increased by 13.1 dB. The proposed two-step OF method is thus demonstrated capable of improving the performance of strain estimation in OF-based elastography.     

Slip elastography: a novel method for visualising and characterizing adherence between two surfaces in contact

Identification of the anatomical location and mechanical properties such as adherence at the tissue tumour interface may be of clinical benefit in determination of tumour resectability and prognosis. There are currently no imaging modalities in routine clinical practice that can provide this information. This paper presents the development of a new imaging technique based on ultrasound elastography, called slip elastography, for determination of the anatomical location and measurement of the adherence between two surfaces. The theoretical basis of slip and its definition in relation to shear are described. In vitro testing with gelatine phantoms to determine the optimal parameters for shear strain estimation and slip boundary measurement and to test reliability are also described.The results suggest that slip elastography can reliably identify the anatomical location of a slip boundary and can measure the externally applied axial force required to initiate slip at that boundary in vitro. The vector based shear strain estimator was the most robust and worked with minimal angular dependence with minimal non-slip shearing artefact.     

A multi-domain Fourier pseudospectral time-domain method for the linearized Euler equations

The Fourier pseudospectral time-domain (F-PSTD) method is computationally one of the most cost-efficient methods for solving the linearized Euler equations for wave propagation through a medium with smoothly varying spatial inhomogeneities in the presence of rigid boundaries. As the method utilizes an equidistant discretization, local fine scale effects of geometry or medium inhomogeneities require a refinement of the whole grid which significantly reduces the computational efficiency. For this reason, a multi-domain F-PSTD methodology is presented with a coarse grid covering the complete domain and fine grids acting as a subgrid resolution of the coarse grid near local fine scale effects. Data transfer between coarse and fine grids takes place utilizing spectral interpolation with super-Gaussian window functions to impose spatial periodicity. Local time stepping is employed without intermediate interpolation. The errors introduced by the window functions and the multi-domain implementation are quantified and compared to errors related to the initial conditions and from the time iteration scheme. It is concluded that the multi-domain methodology does not introduce significant errors compared to the single-domain method. Examples of scattering from small scale density scatters, sound reflecting from a slitted rigid object and sound propagation through a jet are accurately modelled by the proposed methodology. For problems that can be solved by F-PSTD, the presented methodology can lead to a significant gain in computational efficiency.     

Improving motion estimation by accounting for local image distortion

Cardiac elastography is a useful diagnostic technique for detection of heart function abnormalities, based on analysis of echocardiograms. The analysis of the regional heart motion allows assessing the extent of myocardial ischemia and infarction. In this paper, a new two-stage algorithm for cardiac motion estimation is proposed, where the data is taken from a sequence of 2D echocardiograms. The method combines the advantages of block-matching and optical flow techniques. The first stage employs a standard block-matching algorithm (sum of absolute differences) to provide a displacement estimate with accuracy of up to one pixel. At the second stage, this estimate is corrected by estimating the parameters of a local image transform within a test window. The parameters of the image transform are estimated in the least-square sense. In order to account for typical heart motions, like contraction/expansion, translation and rotation, a local affine model is assumed within the test window. The accuracy of the new algorithm is evaluated using a sequence of 500 grayscale B-mode images, which are generated as distorted, but known copies of an original ROI, taken from a real echocardiogram. The accuracy of the motion estimation is expressed in terms of errors: maximum absolute error, root-mean-square error, average error and standard deviation. The errors of the proposed algorithm are compared with these of the known block-matching technique with cross-correlation and interpolation in the sub-pixel space. Statistical analysis of the errors shows that the proposed algorithm provides more accurate estimates of the heart motion than the cross-correlation technique with interpolation in the sub-pixel space.     

Improving motion estimation by accounting for local image distortion

Cardiac elastography is a useful diagnostic technique for detection of heart function abnormalities, based on analysis of echocardiograms. The analysis of the regional heart motion allows assessing the extent of myocardial ischemia and infarction. In this paper, a new two-stage algorithm for cardiac motion estimation is proposed, where the data is taken from a sequence of 2D echocardiograms. The method combines the advantages of block-matching and optical flow techniques. The first stage employs a standard block-matching algorithm (sum of absolute differences) to provide a displacement estimate with accuracy of up to one pixel. At the second stage, this estimate is corrected by estimating the parameters of a local image transform within a test window. The parameters of the image transform are estimated in the least-square sense. In order to account for typical heart motions, like contraction/expansion, translation and rotation, a local affine model is assumed within the test window. The accuracy of the new algorithm is evaluated using a sequence of 500 grayscale B-mode images, which are generated as distorted, but known copies of an original ROI, taken from a real echocardiogram. The accuracy of the motion estimation is expressed in terms of errors: maximum absolute error, root-mean-square error, average error and standard deviation. The errors of the proposed algorithm are compared with these of the known block-matching technique with cross-correlation and interpolation in the sub-pixel space. Statistical analysis of the errors shows that the proposed algorithm provides more accurate estimates of the heart motion than the cross-correlation technique with interpolation in the sub-pixel space.     

一种基于自适应补偿的快速帧速率上转换算法

提出一种基于自适应补偿的快速帧速率上转换算法.算法在塔型结构数据上进行运动估计并利用相邻块运动矢量对上层传递矢量进行修正,减少计算量的同时获得了平滑的运动矢量场.在匹配搜索过程中采用动态调整搜索窗策略,避免了过搜索和搜索不足的问题.运动补偿克服了传统的补偿算法仅采用一种插值方法的不足,根据运动矢量的可靠性分别采用了3种不同的插值方法.为了减少块边缘的失真,采用了重叠块运动补偿的插值方法.在遮挡区域,设计了加权多候选运动矢量插值方法,对前后两帧补偿结果分别赋予不同的权值以减少失真.实验结果表明,该算法与传统算法相比不仅可以大幅度降低计算量,且插值图像的质量有所提高.     

Fast model-based multispectral imaging using nonnegative principal component analysis

Estimation of the spectral reflectance of a scene is a critical problem in image processing and computer vision applications. Model-based multispectral imaging, one of the spectral reflectance estimation methods, can effectively reconstruct the full spectrum using a small number of camera shots. However, it is based on iterative optimization and, thus, is computationally too intensive. In this Letter, we modify the iterative optimization problem to a closed-form problem using nonnegative principal component analysis. The proposed method can substantially reduce the computational cost while maintaining the accuracy.     

Optimal real-time estimation in diffusion tensor imaging

Diffusion tensor imaging (DTI) constitutes the most used paradigm among the diffusion-weighted magnetic resonance imaging (DW-MRI) techniques due to its simplicity and application potential. Recently, real-time estimation in DW-MRI has deserved special attention, with several proposals aiming at the estimation of meaningful diffusion parameters during the repetition time of the acquisition sequence. Specifically focusing on DTI, the underlying model of the noise present in the acquired data is not taken into account, leading to a suboptimal estimation of the diffusion tensor. In this paper, we propose an optimal real-time estimation framework for DTI reconstruction in single-coil acquisitions. By including an online estimation of the time-changing noise variance associated to the acquisition process, the proposed method achieves the sequential best linear unbiased estimator. Results on both synthetic and real data show that our method outperforms those so far proposed, reaching the best performance of the existing proposals by processing a substantially lower number of diffusion images.     

A method of estimating initial conditions of coupled maplattices based on time-varying symbolic dynamics

A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices (CMLs). The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer--Rao lower bound (CRLB) than that with the time-invariant estimation method, especially at high signal-to-noise ratios (SNRs).     

Robust Estimation for Bivariate Poisson INGARCH Models

In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we consider a robust estimation method for bivariate Poisson INGARCH models while using the minimum density power divergence estimator. We demonstrate the proposed estimator is consistent and asymptotically normal under certain regularity conditions. Monte Carlo simulations are conducted to evaluate the performance of the estimator in the presence of outliers. Finally, a real data analysis using monthly count series of crimes in New South Wales and an artificial data example are provided as an illustration.     

A fast tissue stiffness-dependent elastography for HIFU-induced lesions inspection

To monitor HIFU-induced lesion with elastography in quasi-real time, a fast correlation based elastographic algorithm using tissue stiffness–dependent displacement estimation (SdDE) is developed in this paper. The high time efficiency of the proposed method contributes to the reduction on both the number of the displacement points and the computational time of most of the points by utilizing local uniformity of the tissue under HIFU treatment. To obtain admirable comprehensive performance, the key algorithm parameter, a threshold to densify the displacement points, is optimized with simulation over a wedge-inclusion tissue model by compromising the axial resolution (AR) and the computational cost. With the optimum parameter, results from both simulations and phantom experiments show that the SdDE is faster in about one order of magnitude than the traditional correlation based algorithm. At the same time, other performance parameters, such as the signal-to-noise ratio (SNRe), the contrast-to-noise ratio (CNRe) and the axial resolution (AR), are superior to or comparable with that obtained from the traditional algorithm. In vitro experiments on bovine livers validate the improvement on the time efficiency under the circumstances of real tissue and real radio frequency (RF) signal. This preliminary work implies potential of the SdDE in dynamic or close real time guidance and monitoring of HIFU treatment.     

适用于楔形滤光片型光谱成像仪的快速无损数据压缩方法

楔形滤光片型光谱成像仪具有无运动部件、低光机复杂度等优点，是低成本微型化光谱成像仪的一个重要发展方向。不同于传统色散型光谱成像仪，楔形滤光片型光谱成像仪获取的数据是光谱-空间混合调制的图像。针对直接应用CCSDS123进行楔形滤光片型光谱成像仪数据压缩时压缩比较低的问题，结合楔形滤光片型光谱成像仪“谱像混合”、“推扫成谱”的特点，通过定义新的局部差向量，构建了一种低运算复杂度适合硬件实现的快速无损压缩方法WCCSDS123。新的局部差向量中参与计算的像元集合代表的是同一被观测点的光谱信息。WCCSDS123方法首先利用局部和与改进的局部差向量对采样点的值进行预测，再利用预测值与真实值计算预测残差并对其进行整数映射，最后采用采样自适应熵编码对映射预测残差进行编码完成压缩。在6组楔形滤光片型光谱成像仪数据上分别采用WCCSDS123和CCSDS123进行了压缩实验。实验结果表明，与CCSDS123相比，WCCSDS123的压缩比提高了约21.62%，压缩耗时没有明显差异。因此，该方法在提高压缩比同时，继承了CCSDS123复杂度低，易于硬件实现的优点。该方法WCCSDS123具有较低的计算复杂度，能够更加有效地利用空间光谱冗余信息，获得更好的压缩效果，是针对楔形滤光片型光谱成像仪的一种良好的快速无损数据压缩方法。     

Angle-independent and multi-dimensional myocardial elastography--from theory to clinical validation

The angle-independent myocardial elastography, which shows good performance in our proposed theoretical framework using a three-dimensional, ultrasonic image formation model based on well-established, 3D finite-element, canine, left-ventricular models in both normal and left-circumflex ischemic cases, is employed as well as validated in vivo to assess the contractility of normal and pathological myocardia. Angle-independent myocardial elastography consists of: (1) iterative estimation of in-plane and out-of-plane cumulative displacements during systole using 1D cross-correlation and recorrelation techniques in a 2D search; (2) calculation of in-plane finite strains from the in-plane cumulative motion; and (3) computation of in-plane principal strains from the finite strains by eigen decomposition with a classification strategy. The in vivo raw data of healthy and pathological human left ventricles were acquired at 136 fps in a short-axis echocardiographic view. Similar to theory, the elastographic estimates in normal clinical cases showed radial wall thickening and circumferential shortening during systole through principal strain imaging, while those in a pathological case underwent opposite strains. The feasibility of angle-independent myocardial elastography with an automated contour tracking method was hereby demonstrated through imaging of the myocardial deformation, and principal strains were proven essential in the reliable characterization and differentiation of abnormal from normal myocardia, without any angular dependence.     

Ultrasound frame rate requirements for cardiac elastography: experimental and in vivo results

Cardiac elastography using radiofrequency echo signals can provide improved 2D strain information compared to B-mode image data, provided data are acquired at sufficient frame rates. In this paper, we evaluate ultrasound frame rate requirements for unbiased and robust estimation of tissue displacements and strain. Both tissue-mimicking phantoms under cyclic compressions at rates that mimic the contractions of the heart and in vivo results are presented. Sinusoidal compressions were applied to the phantom at frequencies ranging from 0.5 to 3.5 cycles/sec, with a maximum deformation of 5% of the phantom height. Local displacements and strains were estimated using both a two-step one-dimensional and hybrid two-dimensional cross-correlation method. Accuracy and repeatability of local strains were assessed as a function of the ultrasound frame rate based on signal-to-noise ratio values.The maximum signal-to-noise ratio obtained in a uniformly elastic phantom is 20 dB for both a 1.26 Hz and a 2 Hz compression frequency when the radiofrequency echo acquisition is at least 12 Hz and 20 Hz respectively. However, for compression frequencies of 2.8 Hz and 4 Hz the maximum signal-to-noise ratio obtained is around 16 dB even for a 40 Hz frame rate. Our results indicate that unbiased estimation of displacements and strain require ultrasound frame rates greater than ten times the compression frequency, although a frame rate of about two times the compression frequency is sufficient to estimate the compression frequency imparted to the tissue-mimicking phantom. In vivo results derived from short-axis views of the heart acquired from normal human volunteers also demonstrate this frame rate requirement for elastography.     

Pilot design and doubly-selective channel estimation for faster-than-Nyquist signaling

Being capable of enhancing the spectral efficiency (SE), faster-than-Nyquist (FTN) signaling is a promising approach for wireless communication systems. This paper investigates the doubly-selective (i.e., time- and frequency-selective) channel estimation and data detection of FTN signaling. We consider the intersymbol interference (ISI) resulting from both the FTN signaling and the frequency-selective channel and adopt an efficient frame structure with reduced overhead. We propose a novel channel estimation technique of FTN signaling based on the least sum of squared errors (LSSE) approach to estimate the complex channel coefficients at the pilot locations within the frame. In particular, we find the optimal pilot sequence that minimizes the mean square error (MSE) of the channel estimation. To address the time-selective nature of the channel, we use a low-complexity linear interpolation to track the complex channel coefficients at the data symbols locations within the frame. To detect the data symbols of FTN signaling, we adopt a turbo equalization technique based on a linear soft-input soft-output (SISO) minimum mean square error (MMSE) equalizer. Simulation results show that the MSE of the proposed FTN signaling channel estimation employing the designed optimal pilot sequence is lower than its counterpart designed for conventional Nyquist transmission. The bit error rate (BER) of the FTN signaling employing the proposed optimal pilot sequence shows improvement compared to the FTN signaling employing the conventional Nyquist pilot sequence. Additionally, for the same SE, the proposed FTN signaling channel estimation employing the designed optimal pilot sequence shows better performance when compared to competing techniques from the literature.