The exception-maximization algorithm and its application in quantitative remote sensing inversion

Abstract

In remote sensing inversion, we always assume that the observed data error distribution is normal distribution for simplifying the calculation. But under this assumption, only if a few observed data have big error, the inversion result will become unstable. In this paper, we try to use expectation-maximization (EM) algorithm to get more precise and robust inversion result based on another statistical distribution. Linear kernel-driven model with t-distribution error solved by EM algorithm is used to prove this new idea. The inversion methods include traditional ML estimate without prior distribution information of inversion parameters and Bayesian inversion based on prior normal distribution. The test about robustness showed that under the assumption of t-distribution error, more than or over half of observed data have big error can cause instability of inversion results.