边界元法和模拟退火算法在电阻抗断层成像中的应用
Boundary element method and simulated annealing algorithm applied to electrical impedance tomography image reconstruction
摘要：
物理学在医学科学中，特别是在成像诊断中起着基础性的作用。目前，图像重建技术已经在物理课程中教授，并且对新的潜在应用越来越感兴趣。本文的目的是向学生介绍电阻抗断层成像，一种很有前途的技术在医学成像。我们考虑一个数值例子，其中包括在寻找的位置和大小的非导电区域内的导线。我们回顾了电阻抗断层成像逆问题建模的误差泛函的最小化。为了解决在正问题中出现的边值问题，我们使用边界元法。选择模拟退火算法作为优化方法。数值试验表明，该方法对非导电夹杂的反演是准确的。
英文摘要：
Physics has played a fundamental role in medicine sciences, specially in imaging diagnostic. Currently, image reconstruction techniques are already taught in Physics courses and there is a growing interest in new potential applications. The aim of this paper is to introduce to students the electrical impedance tomography, a promising technique in medical imaging. We consider a numerical example which consists in finding the position and size of a non-conductive region inside a conductive wire. We review the electric impedance tomography inverse problem modeled by the minimization of an error functional. To solve the boundary value problem that arises in the direct problem, we use the boundary element method. The simulated annealing algorithm is chosen as the optimization method. Numerical tests show the technique is accurate to retrieve the non-conductive inclusion.
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