Solving inverse problems using Bayesian modeling to incorporate information sources

Inverse problems have been considered unmanageable because they are often ill-posed, i.e., the statement of the problem does not thoroughly constrain the solution space. The authors propose taking 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 to isolate and incorporate causal models as conditional probabilities. As causal models are accurately represented by forward models, the authors propose converting implicit functional models into data driven forward models represented by neural networks, to be used as engines in a Bayesian modeling setting. Satellite remote sensing problems afford numerous opportunities for inclusion of ground truth information, prior probabilities, noise distributions, and other informative constraints within a Bayesian probabilistic framework. The authors apply these methods to an artificial satellite remote sensing problem, comparing the performance to a previously published method of iterative inversion of neural networks