Em algorithm reconstruction of particle size distributions from diffusion battery data

Abstract The EM (Expectation-Maximization) algorithm is presented as a novel method of reconstructing ultrafine particle size distributions from diffusion battery data. The algorithm is an iterative technique for finding maximum-likelihood estimates for grouped particle size distributions. Diffusion battery data were simulated with noise and reconstructions were performed using the EM algorithm and three other methods. In each case the goal was to retrieve known test distributions. Comparison of the reconstructed distributions demonstrated the superiority of the EM algorithm for retrieving particle size information from Poisson-distributed data. The EM algorithm is statistically sound, mathematically simple, and does not require smoothing parameters nor does it impose unnecessary constraints on the solution vector. Due to the algorithm's inherent characteristics, non-negativity and unique convergence of the solution vector are guaranteed.

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