A matrix-free fixed-point iteration for inverting cascade impactor measurements with instrument's sensitivity kernels and hardware

This study focuses on advancing the inversion of aerosol data measured by a cascade impactor. We aim to find and validate a comprehensive and robust mathematical model for reconstructing a particle mass distribution. In this paper, we propose a fixed-point iteration as a method for inverting cascade impactor measurements with relatively simple measurement hardware, which is not optimized for handling advanced linear algebraic operations such as large matrices. We validate this iteration numerically against an iterative L1 norm regularized iterative alternating sequential inversion algorithm. In the numerical experiments, we investigate and compare a point-wise (matrix-free) and integrated kernel-based approach in inverting five different aerosol mass concentration distributions based on simulated measurements and sensitivity kernel functions.