具有反射障碍物的层析成像问题的数学建模与求解
Mathematical Modeling and Solution of the Tomography Problem in Domains with Reflecting Obstacles
AI总结：
本文针对具有反射障碍物的层析成像问题，开发了新的数值方法，通过比较朗伯反射、经典直线射线和镜面反射下的求解性能，表明朗伯反射方法将精度提高一个数量级，镜面反射方法提高约三倍。
摘要：
本工作开发了新的数值方法，用于解决具有反射障碍物的区域中的层析成像问题。我们比较了朗伯反射、经典直线射线层析成像和镜面反射下的求解性能。使用朗伯反射的数值方法相比经典直线射线层析成像，将求解精度提高了一个数量级；而在存在镜面反射障碍物的情况下，数值方法将求解精度提高了大约三倍。我们提出了用于求解软件实现的高效新算法，并分析了求解的性能和有效性。
英文摘要：
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with ubroken rays and for specular reflection. Our numerical method using Lambertian reflection improves the solution's accuracy by an order of magnitude compared to classical tomography with ubroken rays and for tomography in the presence of a specularly reflecting obstacle the numerical method improves the solution's accuracy approximately by a factor of three times. We present efficient new algorithms for the solution's software implementation and analyze the solution's performance and effectiveness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
