Despite the advantages of the moment based methods in solving multivariate population balances models, these methods still suffer with the so-called multivariate moment inversion problem. Although univariate moment inversion is achieved without major problems this is not true for multivariate cases, for which there is no well established methodology. This work presents a comparative analysis of the existing methods regarding their accuracy and robustness. A new moment inversion method based on the independent component analysis was proposed and analyzed. Improvements in accuracy and robustness were achieved by combination of different moment inversion methods. (C) 2013 Elsevier Ltd. All rights reserved.