基于基函数展开方法处理具有陡峭界面的 Abel 反演问题

摘要

在激光聚变研究中,存在大量具有陡峭不连续界面特性的靶丸等离子体诊断问题,需要借助Abel反演方法对结果进行分析。提出了一种基于基函数展开处理不连续径向分布的 Abel 反演方法,采用带约束的 Landweber 迭代法求得优化结果。利用该算法可以对不连续阶跃分布进行比较准确的反演,获得阶跃结构特征。在理想情况下,针对不连续阶跃分布的反演方差好于10-4,即使在存在一定噪声的情况下也仍然可以获得较好的结果。该方法可用于对激光聚变研究中压缩过程中球壳的背光照相、自发光成像、光谱测量等诊断结果的数据分析。%Diagnostics of fusion capsule plasma which usually has a discontinuous radial distribution is a basic problem in la-ser fusion plasma researches.An Abel inversion method based on basis set expansion was proposed to handle this discontinuous Abel inverse problem.This method expands the radial distribution on a set of basis functions,and then the measurement data can be approximated by a linear combination of Abel transforms of the basis functions.The weighted coefficients of the basis functions were obtained by projected Landweber iteration method.Numerical simulations demonstrate that the proposed method is suffi-ciently accurate to reconstruct discontinuous radial distribution,and variance of reconstructed result can reach 10 -4 for ideal sig-nal.Although some noise were added in measurement data,the inversion result can still reflect discontinuous property of radial distribution accurately.