Probabilistic Methods of Inverse Problem Solution

Abstract

This chapter considers the methods of solving the linear discrete inverse problems using the probabilistic approach. We review two major techniques—the maximum likelihood and the maximum a posteriori estimation methods. The Bayes estimation method makes it possible to introduce some a priori information about the properties of the solution in the inversion. We demonstrate that the numerical implementation of these methods is similar to the weighted least-squares and Tikhonov’s regularization methods, respectively. A summary of the typical stochastic inversion techniques, e.g., Monte Carlo, genetic algorithm (GA), and simulated annealing (SA) methods, is also provided.