Abstract This paper provides a critical review of methods used to invert tandem measurements to determine the two-dimensional distribution of particle mass and mobility. We consider the performance of weighted least-squares analysis, Twomey-type approaches, a maximum entropy method, Tikhonov regularization (over a range of regularization parameters), and statistical inversion. A detailed analysis is performed on a bimodal phantom to demonstrate the typical characteristics of reconstructions resulting from the different inversion techniques, before the Euclidean error between the phantom and reconstructions are evaluated for a wider range of phantoms. It is found that 1st order Tikhonov regularization generally outperforms the other established inversion methods, even for narrow phantoms, where the finite representation of the mass-mobility distribution becomes a larger contributor to reconstruction accuracy. Twomey-type approaches, while not as robust, are shown to be an acceptable alternative.

中文翻译：

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确定二维气溶胶质量迁移率分布的反演方法：已建立方法的关键比较

摘要 本文对用于反相串联测量以确定粒子质量和迁移率的二维分布的方法进行了批判性回顾。我们考虑了加权最小二乘分析、Twomey 型方法、最大熵方法、Tikhonov 正则化（在一系列正则化参数上）和统计反演的性能。在对更广泛的体模评估体模和重建之间的欧几里得误差之前，对双峰体模进行了详细分析，以展示由不同反演技术产生的重建的典型特征。发现一阶 Tikhonov 正则化通常优于其他已建立的反演方法，即使对于窄体模，其中质量迁移率分布的有限表示成为重建精度的更大贡献者。Twomey 类型的方法虽然不那么健壮，但已被证明是一种可接受的替代方法。