摘要
超声ＣＴ与Ｘ－ＣＴ的一个重要区别是在通常所用频率范围内物体对声波衍射和反射效应显著。本文根据被层析成象物体内部各点是次级声源的基本事实，从非均匀介质波动方程出发，在Ｂｏｒｎ近似下，应用广义Ｆｏｕｒｉｅｒ切片定理和Ｇｒｅｅｎ函数，并引入相移因子，将运算的参考点取在目标物体上，对散射波原有计算公式作相应变化，导出目标函数与散射场之间的解析关系以及在实际计算时能大大减少重复运算，提高计算速度、缩短处理时间的递归关系式，从而解决了应用微机进行ＣＴ研究时在提高速度与增加占用内存空间之间的矛盾，为在普通微型计算机上快速进行超声层析成象研究提供了可能。由于该方法不要求在空间域或频域中进行插值，故算法本身不引入计算误差。我们据此在ＰＣ机上对不同的模型实现了二维重建模拟成象。成象结果表明，本文提出的加速算法是准确有效的，其成象时间短于其他算法在ＶＡＸ１１／７８０上的ＣＰＵ处理时间。在本文所采用的检测系统模型中，发射和接收换能器均仅沿平行直线移动，避免了常规ＣＴ中复杂的弧线移动，本项工作直接有助于将现有Ｂ超设备改装以进行ＣＴ检测。
It is an important distinction between ultrasonic tomography and X ray tomography that the scattering effect in the interaction between acoustic energy and object, including diffraction and reflection, is very great within normal frequency range used in ultrasonic CT. Based on the basic fact that the internal points of the imaged object are the secondary acoustic sources, a speeded ultrasonic tomography can be achieved in common micro computer after necessary changes in the original formula of scattering wave. Beginning with equation of proqagation in an inhomogeneous medium under Born approximation, applying the generalized Fourier slice theorem and Green function, introducing the phase shift factor, and taking the reference point of computation at the object, we derive an analytic relation between scattering field and object function. A recursion formula applied to increasing the computational speed and decreasing the comutational time by avoiding a great deal of repetitive calculation in practical reconstruction is also presented in this work. This improvement solves the inconsistency between the increment of speed and that of memory occupancy in the study of CT on micro computer so that it makes possible taking ultrasonic diffraction tomography research fast on common micro computer. Without interpolations in either the frequency or the space domain, no computational errors are introduced by the algorithm itself. To demonstrate the numerical accuracy of the algorithm, we performed some two dimensional simulation reconstruction for various models on PC system according to the formulae above. The results of imaging show that the speeding algorithm presented in this paper is accurate and efficient and the treating time of this method on PC is shorter than that of other algorithms for ultrasonic CT on VAX 11/780 system. Furthermore, the tomography imaging system introduced here requires the transmitting and receiving transducer moving just along with two parallel lines instead of complex arc moving in ordinary CT system. The above work will contribute directly to improving the existing B Ultrasonic evaluation system for computer tomography application to common micro computer.
出处
《南京大学学报（自然科学版）》
CSCD
1996年第2期224-230,共7页
Journal of Nanjing University（Natural Science）
基金
国家自然科学基金
