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. 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 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. The forward model merges the information from an analytic model of estimated accuracy and a limited number of ground truth information, which are true samples of the function under study. We apply these methods to satellite remote sensing problems, as they afford numerous opportunities for inclusion of ground truth information, prior probabilities, noise distributions, and other informative constraints.; In particular, this dissertation elaborates an indepth Bayesian analysis of inverse problems, including novel aspects such as ground truth incorporation and the use of embedded neural networks. The model ground truth incorporation is accomplished through a novel kernel technique, where the analysis of the new technique proves as fruitful as the technique itself. Finally, these methods are validated in simulation, and applied to a real world problem of inverse geophysical parameter retrieval for Africa using satellite data.