Solving inverse problems by Bayesian iterative inversion of a forward model with ground truth incorporation

Inverse problems have been often considered ill-posed, i.e., the statement of the problem does not thoroughly constrain the solution space. In this paper we take advantage of this lack of information by adding additional informative constraints to the problem solution using Bayesian methodology. Bayesian modeling gains much of its power from its ability 2 to isolate and incorporate causal models as conditional probabilities. As causal models are accurately represented by forward models, we convert implicit functional models into data driven forward models represented by neural networks, to be used as engines in a Bayesian modeling setting. Remote sensing problems aaord opportunities for inclusion of ground truth information, prior probabilities, noise distributions, and other informative constraints within a Bayesian probabilistic framework. We apply these Bayesian methods to a synthetic remote sensing problem, showing that the performance is superior to a previously published method of iterative inversion of neural networks. In addition, we show that the addition of ground truth information, naturally included through Bayesian modeling, provides a signiicant performance improvement.