Problems by Bayesian Iterative Inversion of a Forward Model with Applications to Parameter Mapping Using SMMR Remote Sensing Data

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 to isolate and incorporate causal models as conditional probabil- ities. 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 afford opportunities for inclusion of ground truth information, prior probabilities, noise distributions, and other informative constraints within a Bayesian probabilistic framework. We first 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. Next, microwave brightness temperatures obtained from the Scanning Multichannel Microwave Radiometer (SMMR) over the African continent are inverted. The values of soil moisture, surface air temperature and vegetation moisture retrieved from the inversion produced contours that agree with the expected trends for that region.