Local estimators and Bayesian inverse problems with non-unique solutions

Bayesian approach is effective for inverse problems. The posterior density distribution provides useful information of the unknowns. However, problems with non-unique solutions, classical estimators such as maximum a (MAP) and conditional mean (CM) are not suitable. We introduce two new estimators, local (LMAP) (LCM). A simple algorithm based on clustering to compute LMAP LCM proposed. Their applications demonstrated by three problems: an spectral problem, source medium problem.