Improved Inversion of Scanning Electrical Mobility Spectrometer Data Using a New Multiscale Expectation Maximization Algorithm

Abstract

The accuracy of particle size distributions obtained from scanning electrical mobility spectrometer (SEMS) measurements is strongly dependent on the accurate consideration of the instrument characteristics in the formulation of the SEMS problem and the effective inversion of the resulting SEMS equation. The estimation of size distributions from SEMS measurements requires a solution of the discretized form of the Fredholm integral equation of the first kind. The often ill-conditioned nature of the linear inverse problem coupled with the possible presence of measurement noise complicates these calculations. The use of standard inversion approaches, such as nonnegative least squares (NNLS) or regularization-based algorithms, requires SEMS measurements with significant signal-to-noise ratio or some a priori knowledge of the shape of the sampled size distribution. These severe constraints for SEMS measurements can be relaxed with the new multiscale expectation-maximization SEMS inversion method introduced here...