DEALING WITH INCONSISTENT MEASUREMENTS IN INVERSE PROBLEMS: SET-BASED APPROACH

摘要

The inverse problem consists of retrieving back the parameter values of a physical model given a set of measurements. This problem becomes ill-posed as soon as errors happen in either the model or the measurements, at which steps one needs to specify a method to retrieve a solution. While several such methods exist in the literature, most of them use least-square minimization or Bayesian approaches. In this paper, we explore how set-based approaches can be useful to obtain a solution to the inverse problem, in particular, when measurements are inconsistent with each other. Our approach intrinsically differs from the previously mentioned ones, as it does not rely on the idea of minimizing the average error, but rather on selecting a subset of consistent measurements. We show with a set of experiments that this is particularly interesting when some measurements can be suspected of being outliers.