Ultrasound Tomography has seen a revival of interest in the past decade, especially for breast imaging, due to improvements in both ultrasound and computing hardware. In particular, three-dimensional ultrasound tomography, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray ultrasound tomography in 3D for a hemispherical detector array is presented. Two ray-tracing approaches are derived and compared. More significantly, the problem of linking the rays between emitters and receivers, which is challenging in 3D due to the high number of degrees of freedom for the trajectory of rays, is analysed both as a minimisation and as a root-finding problem. The ray-linking problem is parameterised for a convex detection surface and three robust, accurate, and efficient ray-linking algorithms are formulated and demonstrated. To stabilise these methods, novel adaptive-smoothing approaches are proposed that control the conditioning of the update matrices to ensure accurate linking. The nonlinear UST problem of estimating the sound speed was recast as a series of linearised subproblems, each solved using the above algorithms and within a steepest descent scheme. The whole imaging algorithm was demonstrated to be robust and accurate on realistic data simulated using a full-wave acoustic model and an anatomical breast phantom, and incorporating the errors due to time-of-flight picking that would be present with measured data. This method can used to provide a low-artefact, quantitatively accurate, 3D sound speed maps. In addition to being useful in their own right, such 3D sound speed maps can be used to initialise full-wave inversion methods, or as an input to photoacoustic tomography reconstructions.

中文翻译：

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用于乳房三维超声断层扫描的基于折射校正的射线反演

由于超声和计算硬件的改进，超声断层扫描在过去十年中重新引起了人们的兴趣，尤其是在乳房成像方面。特别是三维超声断层扫描，一种将要成像的介质被超声换能器包围的全断层扫描方法，已经变得可行。在本文中，对半球形探测器阵列的 3D 大型弯曲射线超声断层扫描的稳健框架进行了全面推导和研究。导出并比较了两种光线追踪方法。更重要的是，将发射器和接收器之间的光线连接起来的问题，由于光线轨迹的大量自由度而在 3D 中具有挑战性，被分析为最小化和寻根问题。光线链接问题针对凸检测表面进行了参数化，并制定并演示了三种稳健、准确且高效的光线链接算法。为了稳定这些方法，提出了新的自适应平滑方法来控制更新矩阵的条件以确保准确链接。估计声速的非线性 UST 问题被重新定义为一系列线性化子问题，每个子问题都使用上述算法并在最速下降方案内解决。整个成像算法在使用全波声学模型和解剖乳房模型模拟的真实数据上被证明是稳健和准确的，并结合了测量数据中可能存在的飞行时间拾取误差。该方法可用于提供低伪影、定量准确、3D 声速图。除了本身很有用之外，这种 3D 声速图还可用于初始化全波反演方法，或作为光声断层扫描重建的输入。