基于折射校正的射线反演的乳腺三维超声断层成像
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast
摘要：
在过去的十年中，由于超声和计算硬件的改进，超声断层扫描技术已经重新受到人们的关注，特别是对于乳腺成像。特别地，三维超声断层摄影，其中待成像的介质被超声换能器包围的完全断层摄影方法，已经变得可行。在本文中，一个全面的推导和研究的一个强大的框架，大规模的X射线超声断层扫描在三维半球形探测器阵列。两种射线追踪方法推导和比较。更重要的是，在发射器和接收器之间链接射线的问题，这是具有挑战性的3D由于大量的自由度的射线的轨迹，分析作为一个最小化和作为一个寻根问题。射线连接问题的参数化凸检测表面和三个强大的，准确的，高效的射线连接算法制定和证明。为了稳定这些方法，提出了新的自适应平滑方法，控制更新矩阵的条件，以确保准确的链接。估计声速的非线性UST问题被改写为一系列线性化子问题，每个子问题使用上述算法和最速下降方案求解。整个成像算法被证明是鲁棒性和准确性的真实数据模拟使用全波声学模型和解剖乳房体模，并纳入由于飞行时间挑选的误差，将与测量数据。该方法可用于提供低伪影、定量准确的3D声速图。除了本身有用之外，这种3D声速图还可以用于初始化全波反演方法，或者作为光声层析成像重建的输入。
英文摘要：
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.
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