A non-homogeneous regularization method for the estimation of narrow aerosol size distributions

The determination of particle size distributions from e.g. DMPS or TDMA measurements is an ill-posed problem that is often solved using regularization methods. With Tikhonov-type regularization the standard smoothness assumptions may yield infeasible estimates for the size distribution in cases where the size distribution contains narrow peaks. In this paper we propose a method for the estimation of size distributions with narrow peaks. The method is based on the utilization of a weight function to modify the standard smoothness constraints to obtain nonhomogeneous smoothing effect. In the problem formulation prior assumptions about the weight function are exploited and the size distribution and the weight function can be estimated simultaneously. The performance of the method is evaluated with simulated TDMA data and the results show that good agreement between the estimates and the true size distributions can be achieved. (C) 2000 Elsevier Science Ltd. All rights reserved.