The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets for both absolute and time-difference imaging, when large portions of the domain are inaccessible for measurement. As most medical applications of electrical impedance tomography are limited to partial boundary data, the development of partial boundary algorithms is highly desirable. While iterative schemes have been used traditionally, their high computational cost makes them cost-prohibitive for applications that need fast imaging. The proposed algorithms require no iteration and provide informative absolute or time-difference images exceptionally quickly in under 2 seconds. Reconstructions are compared to reference reconstructions from standard linear difference imaging (30 seconds) and total variation regularized absolute imaging (several minutes) The algorithms perform well under high levels of noise and incorrect domain modeling.

翻译：本文首次针对三维电阻抗成像问题，开发并测试了基于复几何光学方法的部分边界数据重建算法，并在仿真与实验数据上进行了验证。当测量区域大部分不可达时，该方法在绝对成像与时间差分成像中均能实现对目标的有效定位。由于电阻抗成像在医疗领域中的应用大多受限于部分边界数据，开发部分边界算法具有重要价值。传统方法通常采用迭代方案，但其高昂的计算成本使其难以满足快速成像需求。本文提出的算法无需迭代，可在2秒内快速生成信息丰富的绝对或时间差分成像结果。重建效果与标准线性差分成像（30秒）及全变分正则化绝对成像（数分钟）的参考重建结果进行了对比。该算法在高噪声水平及不精确区域建模条件下仍表现出良好性能。