由線性彈性模型引起的多維系數反問題在很多範疇都有其應用，如斷層探測、油田檢測、鹽石檢測、礦石檢測及醫療成像等。瞬時成像技術是其中最有用的應用。它提供了一個快速及安全的醫療成像技術，可以用來檢測在身體內快速移動的器官的一些異常組織，如肝腫瘤。在這篇論文中，我們會重點討論兩個解決瞬時弹性成像反問題的數值方法，即水平集反演方法和近似全局收斂方法。我們會研究這兩種方法的推導和數值結果。 / 特別地，近似全局收斂方法是一種由Klibanov 新提出用來解決由雙曲偏微分引起的多維系數反問題的方法。因為這佪方法沒有使用求泛函極小值的步驟，因此能避免了一些眾所周知的問題，所以它特別穩定。數值結果顯示近似全局收斂方法對噪聲有很高的穩定性。這表明近似全局收斂方法是一個解決由線性彈性模型引起的多維系數反問題的其中一個有效方法。 / Multi-dimensional coefficient inverse problem (MCIP) in linear elasticity has found many applications, such as crack detection, oil/salt/ore detection, medical imaging. Transient elastography is among one of the most useful applications, providing a fast and safe medical imaging technique which can be used to detect tumors or abnormal tissue in “fast-moving“ organs such as the liver. In this thesis focus is casted on two of the numerical algorithms to solve inverse problems related to transient elastography, namely the level-set inversion method and the approximate globally convergent method. The derivations of both methods and numerical results are presented. In particular, the approximate globally convergent method is a newly developed stable method to solve coefficient determination inverse problem for hyperbolic partial differential equation proposed by Beilina and Klibanov in [6]. It achieves pproximately a global convergence by avoiding construction of a least squares functional, thus averting some of the well-known problems of trapping in the neighborhoods of local minima when one minimizes such a nonlinear functional. The results of the approximate globally convergent method have shown its strong stability and robustness. This suggests a good way for the reconstruction of the distribution of the shear modulus in the coefficient inverse problem of linear elasticity. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chow, Yat Tin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 98-102). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Linear Elasticity Model --- p.9 / Chapter 2.1 --- Introduction to Linear Elasticity Model --- p.9 / Chapter 2.2 --- Physical Meanings of Elasticity Equation --- p.12 / Chapter 2.3 --- Derivations of Linear Elasticity Equation --- p.14 / Chapter 2.4 --- Discussion of Christoffel’s Equation --- p.17 / Chapter 3 --- Formulations of the Forward and Inverse Problem --- p.27 / Chapter 3.1 --- The Forward Problem --- p.29 / Chapter 3.2 --- The Inverse Problem --- p.29 / Chapter 3.3 --- A Uniqueness Result --- p.30 / Chapter 4 --- Algorithms for Inverse Problems in Elasticity --- p.33 / Chapter 5 --- Level Set Inversion Method --- p.37 / Chapter 5.1 --- Arrival Time Acquisition: Cross-Correlation --- p.37 / Chapter 5.2 --- The Distance Inversion Method --- p.41 / Chapter 5.3 --- Solving the Forward Eikonal Equation --- p.43 / Chapter 5.3.1 --- Discretizing the eikonal equation --- p.43 / Chapter 5.3.2 --- A forward eikonal solver: fast marching algorithm --- p.47 / Chapter 5.3.3 --- A forward eikonal solver: fast sweeping algorithm --- p.50 / Chapter 5.4 --- Level Set Inversion Scheme --- p.54 / Chapter 5.5 --- Numerical Implementation --- p.57 / Chapter 5.6 --- Results of Reconstructions --- p.58 / Chapter 6 --- Approximate Globally Convergent Method --- p.63 / Chapter 6.1 --- The Forward Problem --- p.65 / Chapter 6.1.1 --- Forward problem in time domain --- p.65 / Chapter 6.1.2 --- Forward problem in Laplace domain --- p.67 / Chapter 6.2 --- The Inverse Problem --- p.67 / Chapter 6.2.1 --- Inverse problem in time domain --- p.67 / Chapter 6.2.2 --- Inverse problem in Laplace domain --- p.68 / Chapter 6.3 --- A Nonlinear Integral Differential Equation --- p.69 / Chapter 6.4 --- Approximation of the First Tail --- p.71 / Chapter 6.5 --- The Algorithm --- p.72 / Chapter 6.6 --- Notes About the Convergence Analysis --- p.76 / Chapter 6.6.1 --- Approximate global convergence --- p.76 / Chapter 6.6.2 --- Basic formulation of Theorem 2.9.4 of [6] --- p.78 / Chapter 6.6.3 --- Some ideas of the convergence analysis for the algorithm in section 6.5 --- p.80 / Chapter 6.7 --- Numerical Implementation --- p.81 / Chapter 6.8 --- Results of Reconstructions --- p.88 / Chapter 7 --- Conclusions --- p.96 / Bibliography --- p.98

在各种临床应用广泛使用的诊断和治疗工具中，超声成像是其中的一个。与其他成像模式相比，比如计算机断层照相法和磁共振成像，超声波检查法有许多优点:没有辐射风险，设备价格低以及能够实时获取图像。很多超声应用的第一步通常是对感兴趣组织和结构的检测和定位。然而，超声图像存在一些特有的伪影，比如高噪声，低信噪比和灰度不均，这些伪影使得检测任务变得困难。此外，感兴趣区域之间的低对比度也使得这一任务变得更加复杂。在这篇论文里，我们深入研究这些图像伪影并提出新的方法来促进临床中的超声应用。 / 首先，我们提出一个多尺度的框架来进行超声图像的分割，这个框架是基于各向异性去噪扩散和测地主动轮廓线的。各向异性去噪扩散是对边缘敏感且专门用于斑点噪声图像的扩散过程，这里它被用来去除超声图像的斑点噪声，我们对每幅输入图像构造一个多尺度的表示方法，随着尺度的增加，噪声被逐渐地消除。之后，多尺度测地主动轮廓线从粗到细渐进地应用到这些尺度来提取物体的边界线。为了避免在低对比度区域出现边界泄漏的情况，我们把不同尺度之间的边界形状相似性结合到传统的测地主动轮廓线模型里作为一个外部约束来指导轮廓线的演化。在合成和临床图像的实验结果证明了我们的方法的优越性。 / 其次，我们提出一个基于相位的方法来检查和测量超声图像里的胎儿腹部轮廓线。我们定义了一个基于局部相位的度量来检测胎儿腹部的边界线，这个度量称为多尺度特征非对称性，它与图像的亮度无关，并且能为图像里特征的重要程度提供一个绝对的测量。为了估计与腹部轮廓线相吻合的椭圆，我们使用一个迭代随机霍夫变换来排除内腹部边界线的影响，从而使得估计的椭圆逐渐收敛到外边界线。在临床超声图像里进行腹部周长测量的实验结果验证了我们的方法与手工的方法有很高的一致性，这也表明我们的方法可以作为一个可靠的工具来进行产科的护理和诊断。 / Ultrasound imaging is one of the most widely used diagnostic and therapeutic tools for a variety of clinical applications. Compared with other imaging modalities, such as computed tomography and magnetic resonance imaging, ultrasonography has a lot of advantages: free of radiation risk, low cost of acquisition and images are available in real-time. The first step in many ultrasonic applications is usually the detection and localization of interested tissues and structures. However, there are a number of characteristic artifacts in ultrasound images that make the task difficult such as high speckle noise, low signal-to-noise ratio and intensity inhomogeneity. Besides, the low contrast between regions of interest further complicates the processing. In this thesis, we deeply investigate these image artifacts and propose new techniques to facilitate ultrasonic applications in clinic. / First, we propose a multiscale framework for ultrasound image segmentation based on speckle reducing anisotropic diffusion(SRAD) and geodesic active contours (GAC). SRAD is an edge-sensitive diffusion tailored for speckled images, and it is adopted here to reduce speckle noise by constructing a multiscale representation for each input image, where the noise is gradually removed as the scale increases. Multiscale geodesic active contours are then applied along the scales in a coarse-to-fine manner to capture the object boundaries progressively. To avoid boundary leakages in low contrast regions, traditional GAC model is modified by incorporating the boundary shape similarity between different scales as an external constraint to guide the contour evolution. Experimental results in both synthetic and clinical images demonstrate the superiority of the proposed approach. / Second, we propose a phase-based approach for fetal abdominal contour detection and measurement in ultrasound images.We define a local phase-based measure, called multiscale feature asymmetry (MSFA), from the monogenic signal to detect the boundaries of fetal abdomen. The MSFA measure is intensity invariant and provides an absolute measurement for the significance of features in the image. In order to estimate the ellipse that fits to the abdominal contour, we employ an iterative randomized Hough transform to exclude the interferences of the inner boundaries of the abdomen, after which the estimated ellipse gradually converges to the outer boundaries. Experimental results in clinical ultrasound images validate the high agreement between our approach and manual approach in the measurement of abdominal circumference, indicating that the proposed approach can be used as a reliable tool for obstetric care and diagnosis. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Weiming . / Thesis (Ph.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 68-84). / Abstracts also in Chinese. / Wang, Weiming .

The ability to numerically determine the received signal in an ultrasound pulse-echo system is very important for the development of new ultrasound applications, such as tissue characterization, complex object recognition, and identification of surface topology. The output signal from an ultrasound pulse-echo system depends on the transducer geometry, reflector shape, location and orientation, among others, therefore, only by numerical modeling can the output signal for a given measurement configuration be predicted. This thesis concerns about the numerical modeling and optimal design of annular array based ultrasound pulse-echo system for object recognition. Two numerical modeling methods have been implemented and evaluated for calculating received signal in a pulse-echo system. One is the simple, but computationally demanding Huygens Method and the other one is the computationally more efficient Diffraction Response for Extended Area Method (DREAM). The modeling concept is further extended for pulse-echo system with planar annular array. The optimal design of the ultrasound pulse-echo system is based on annular array transducer that gives us the flexibility to create a wide variety of insonifying fields and receiver characteristics. As the first step towards solving the optimization problem for general conditions, the problem of optimally identifying two specific reflectors is investigated. Two optimization methods, the straightforward, but computationally intensive Global Search Method and the efficient Waveform Alignment Method, have been investigated and compared.

The present study utilizes the ultrasonic travel time technique to diagnose grid generated turbulence. Ultrasonic flow metering technology relies on the measurement and computation of small perturbations in the travel time of acoustic ultrasonic waves through the dynamic medium. The statistics of the travel time variations of ultrasonic waves that are caused by turbulence probably affect the performance of ultrasonic flow meters. Motivation for the study stems from the large travel time variations observed in typical ultrasonic flow and circulation meters. Turbulent flow data was collected downstream of a grid introduced in a uniform flow in the wind tunnel using ultrasonic techniques. Grid turbulence is well defined in literature, and is nearly homogeneous and isotropic. The experimental investigation was performed under well-controlled laboratory conditions. The grid mesh sizes varied from 0.25-0.5in, and flow velocities from 0-20m/s. The ultrasonic transducers were of 100 kHz working frequency; and all of the data was collected with them oriented perpendicular to the mean flow. Path lengths were increased from 2-10in; and the data acquisition and control system featured a very high speed data acquisition card with an analog to digital converter that enabled excellent resolution of ultrasonic signals. Experimental data was validated by comparison to other studies. The work aims to investigate the influence of the grid-generated turbulent flow on acoustic wave propagation, in terms of the variance of the travel time. The effect of turbulence on acoustic wave propagation was observed. The experimental data was used to compute average travel times, acoustic travel time variances, and standard deviation amplitude fluctuations. The data was collected in the region estimated to be homogeneous and isotropic. Average travel time data support the assumption that only the large (as compared to the wavelength ) turbulent inhomogeneities influence acoustic wave propagation. Variance data confirm the presence of a non-linear trend in the acoustic travel times with increasing path length. Amplitude fluctuations data confirm a correlation between areas of caustic formation and large amplitude fluctuations.

"The condensation of vapor onto a cooled surface is a phenomenon which can be difficult to quantify spatially and as a function of time; this thesis describes an ultrasonic system to measure this phenomenon. The theoretical basis for obtaining condensate film thickness measurements, which can be used to calculate growth rates and film surface features, from ultrasonic echoes will be discussed and the hardware and software will be described. The ultrasonic system utilizes a 5MHz planar piston transducer operated in pulse-echo mode to measure the thickness of a fluid film on a cooled copper block over the fluid thickness range of 50 microns to several centimeters; the signal processing algorithms and software developed to carry out this task are described in detail. The results of several experiments involving the measurement of both non-condensing and condensing films are given. In addition, numerical modeling of specific condensate film geometries was performed to support the experimental system; the results of modeling nonuniform fluid layers are discussed in the context of the effect of such layers on the measurement system."

"Abstract Conventional ultrasound imaging systems use array transducers for focusing and beam steering, to improve lateral resolution and permit real-time imaging. This thesis research investigates a different use of array transducers, where the acoustic field and the receiver characteristics are designed such that the energy of the output signal from targets of a specified geometry is maximized. The output signal is the sum of the received signals obtained using all the possible combinations of transducer array elements as transmitter and receiver. This work is based on annular array transducers, but is applicable for any array configuration. The first step is the development of software for the efficient modeling of the wave interaction between transmitted field and target, and between the transducer and receiver field. Using this software, we have calculated the received signal for each combination of an array element as transmitter and the same or another array element as receiver, leading to an N x N received signal matrix for an N element array transducer. A waveform optimization algorithm is then implemented for the purpose of determining the set of delays for the individual array elements, which maximizes the energy of the sum of the received signals. In one implementation of this algorithm, the received signal with the maximum energy is considered as a reference signal, and specific delays are applied to the other signals so that any two signals produce a maximum correlation. This leads to an N x N delay matrix, which, however, is not readily implemented in a practical real-time system, which uses all the elements in an array transducer simultaneously to customize acoustic fields. Hence, the values in this delay matrix are fed into a linear programming optimizer tool to obtain a set of delay values, which makes its implementation practical. The optimized set of delays thus obtained is used to maximize the energy of the received signal for a given transducer and target geometry and hence to enhance the reflectivity of that target. It is also important to check the robustness of the optimized set of delays obtained above, for a given target geometry. Robustness refers to the sensitivity of the optimization to variation in target geometry. This aspect is also evaluated as a part of this thesis work."

"This thesis documents the experimental proof of concept study for an ultrasonic method of wake vortex detection. A new acoustic technique is utilized to measure the circulation produced in the wake of lift-generating aircraft. Ultrasonic signals are transmitted in a path around the wake vortex, and are used to determine the average in-line velocity component along the acoustic path. It is shown herein that this velocity component is directly proportional to the net circulation value within the acoustic path. This is the first study to take this methodology and implement it in a realistic airport setting. This project included constructing a prototype and conducting field tests to prove the validity of this technology in a realistic environment setting. During field tests an acoustic path enclosed the vorticity shed behind one wing of a Piper PA-28 aircraft. Fourteen initial test flights were conducted in calm atmospheric conditions, and results show circulation values measured are comparable in magnitude and direction to expected circulations generated by the Piper PA-28 aircraft. Additional testing in various atmospheric conditions revealed the scope of practice for such a measurement technology. This study demonstrates the validity of the acoustic method in detecting aircraft wake vortices. Future investigations and applications utilizing this technique are discussed within."

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Une analyse numérique basée sur la méthode des éléments finis permettant de quantifier les coefficients d'atténuation et de diffusion ultrasonores dans un polycristal en domaine temporel et fréquentiel est présentée. En particulier, une méthode originale basée sur le théorème de réciprocité pour l'évaluation numérique du coefficient de diffusion est proposée. Des formules analytiques bidimensionnelles (2D) pour les coefficients d'atténuation ultrasonore et de rétrodiffusion sont développées en utilisant l'approximation de Born pour valider les évaluations numériques. L'approche numérique proposée est appliquée au titanium, un polycristal monophasé et non texturé. Premièrement, des simulations sont effectuées dans des microstructures idéalisées composées de grains en taille unimodale. Une comparaison cohérente entre les évaluations numériques et les prédictions analytiques 2D est obtenue. Par ailleurs, les effets de l'atténuation induite par la diffusion multiple sur la mesure de rétrodiffusion, qui sont négligés par les modèles théoriques, sont quantifiés. Deuxièmement, l'approche numérique proposée est appliquée aux polycristaux composés de grains en taille bimodale. Les résultats numériques indiquent que les coefficients d'atténuation et de rétrodiffusion en domaine fréquentiel se situent au milieu des coefficients pour les microstructures unimodales et sont principalement déterminés par les fractions volumiques des grains constitutifs. Cependant, ils ne sont que légèrement affectés par la répartition des gros grains. Une étude de la fonction d'autocorrélation spatiale dans des telles microstructures bimodales est proposée afin d’obtenir une interprétation analytique des phénomènes expérimentés numériquement. / A numerical approach based on the finite element method to quantify ultrasonic attenuation and grain-noise scattering coefficients in both time and frequency domains for polycrystalline materials is presented. More particularly, an original method based on the reciprocity theorem for the numerical evaluation of the grain-noise scattering coefficient is proposed. Twodimensional (2D) analytical formulas of ultrasonic attenuation and backscattering coefficients are developed by using the Born approximation to validate numerical evaluations. Then the proposed numerical approach is applied to the single-phase and untextured polycrystalline titanium. Firstly, 2D FE simulations are performed in idealized microstructures composed of equiaxed grains with different unimodal grain sizes. Coherent comparison between numerical estimates and 2D analytical predictions is obtained. Effects of attenuation due to multiple scattering on the backscattering measurement, which are neglected in the theoretical model, are quantified. Secondly, polycrystals with bimodal grain sizes are considered. Numerical results indicate that attenuation and backscattering coefficients in bimodal microstructures are inbetween the ones of unimodal microstructures and are mainly determined by volume fractions of the constituent grains. However they are only slightly affected by the grain location distributions. The spatial autocorrelation function in bimodal microstructures is further quantified to gain an analytical interpretation of the above phenomena.

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 67-68. / M.S.