核能安全生产过程中，详细的三维辐射场剂量率信息对于优化辐射防护和规划放射性区域的工作非常重要。在稀疏和不规则的测量点情况下，反演方法的研究获得了关注。现有反演方法主要集中于二维辐射场剂量率的反演和规则网格上进行反演，无法用于获得稀疏测点下三维辐射场的剂量率信息。本文在系统概述国内外现有辐射场反演算法背景和现状，以及基于偏微分方程的图像修复算法现状后，提出了新的基于修正的Cahn-Hilliard方程的反演方法和基于TV-H-1方程的反演方法并给出每种方法的数值求解格式，通过迭代计算恢复辐射场剂量率分布，能够在稀疏和任意位置的测量数据下，重建三维伽马辐射场剂量率信息。为验证提出反演方法的可靠性并评估反演结果。本文使用FLUKA软件对一现实放射性废物处理设施不同假设工况下的辐射场进行了蒙特卡罗模拟。本文通过对模拟的三维辐射场剂量率分布进行随机和规则采样，获得稀疏的辐射场测点数据，并用两种反演方法分别对取样数据进行了反演。最终将反演结果与原模拟辐射场结果对比进行评估。本文还对一维方向上的真实剂量率数据进行了反演，并与蒙特卡罗模拟结果做对比，以验证本文所提出方法在真实情况下的可用性。对于基于修正的Cahn-Hilliard方程的反演方法，本文提出在修正的Cahn-Hilliard方程模型中引入了三维曲率函数以实现对辐射场剂量率连续值的恢复。验证案例表明，基于修正的Cahn-Hilliard方程模型的反演方法在随机和规则采样情况下都能达到令人满意的精度，前者在4.12%，后者在3.9%的采样率下的数据能够实现无屏蔽情况下对单源辐射场反演相对误差低于6.23%，实现包含屏蔽情况下的反演相对误差在6.78%-10.03%区间之间。该方法规则采样下的反演结果要稍微好于随机采样的反演结果。对于基于TV-H-1方程的反演方法，很好地重建了包含不同数量放射源辐射场的剂量率分布特征和数值分布，并在采样率仅为3.125%的情况下反演出了高度准确的完整辐射场数据。所有验证案例下该方法的平均相对误差在2.18%-2.70%之间，随机采样和规则采样这两种采样策略下该方法的辐射场反演表现非常相似。两种方法在一维方向上对实测数据的反演都表明其在本文研究案例下相对于蒙特卡罗方法有更好的适用性。
Detailed three-dimensional radiation field dose rate information is very important for the optimization of radiation protection and planning of radioactive areas during the safe production of nuclear energy. In the case of sparse and irregular measurement points, the study of inversion methods has gained attention. The existing inversion methods mainly focus on inversion of two-dimensional radiation field dose rates and inversion on regular grids, which cannot be used to obtain three-dimensional radiation field dose rate information under sparse measurement points.In this paper, after systematically outlining the background and status of existing radiation field inversion algorithms at home and abroad, and the status of image inpainting algorithms based on partial differential equations, a new inversion method based on the modified Cahn-Hilliard equation and an inversion method based on the TV-H-1 equation are proposed and the numerical solution scheme of each method is given, and the radiation field dose rate distribution is recovered by iterative computation, which is able to recover the radiation field dose rate distribution and the three-dimensional gamma radiation field dose rate information can be reconstructed under sparse and arbitrary location of measurement data. To verify the reliability of the proposed inversion method and to evaluate the inversion results, Monte Carlo simulations of the radiation field of a real radioactive waste disposal facility under different assumptions of operating conditions are performed by using FLUKA software. In this paper, sparse radiation field measurement point data are obtained by random and regular sampling of the simulated three-dimensional radiation field dose rate distribution, and the sampled data are used to inverse the radiation field by two inversion methods. The final inversion results are evaluated in comparison with the original simulated radiation field results. In this paper, the real dose rate data in the one-dimensional direction are also used into inversion and compared with the Monte Carlo simulation results to verify the usability of the proposed method in real situations.For the inversion method based on the modified Cahn-Hilliard equation, this paper introduces a three-dimensional curvature function into the modified Cahn-Hilliard equation model to achieve the recovery of continuous values of radiation field dose rates. The validation cases show that the inversion method based on the modified Cahn-Hilliard equation model can achieve satisfactory accuracy in both random and regular sampling cases, with the sampling rate at 4.12% with random samples and 3.9% with regular samples to achieve a relative error of less than 6.23% for the single-source radiation field inversion without shielding, and a relative error of 6.78%-10.03% for the inversion with shielding. The relative error of the inversion with shielding is in the range of 6.78%-10.03%. The inversion results of the method with regular sampling are slightly better than those with random sampling. For the inversion method based on the TV-H-1 equation, the dose rate distribution characteristics and numerical distribution of the radiation field containing different numbers of sources are well reconstructed, and the complete radiation field data are reconstructed with high accuracy at a sampling rate of only 3.125%. The average relative error of the method is between 2.18% and 2.70% for all validation cases, and the performance of the radiation field inversion is very similar for the two sampling strategies, random sampling and regular sampling. The inversions of the measured data in the one-dimensional direction for both methods show their better applicability compared to the Monte Carlo method in cases in this paper.
