Inversion methods to determine two-dimensional aerosol mass-mobility distributions: A critical comparison of established methods

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.