Solving inverse problems by Bayesian neural network iterative inversion with ground truth incorporation

Neural networks have long been applied to inverse parameter retrieval problems. The literature documents a development from the use of neural networks as explicit inverses to neural network iterative inversion (NNII) and, finally, to Bayesian neural network iterative inversion (BNNII), which adds a Bayesian superstructure to NNII. Inverse problems have been often considered ill posed, i.e. the statement of the problem does not thoroughly constrain the solution space. BNNII takes advantage of this lack of information by adding additional informative constraints to the problem solution using Bayesian methodology. This paper extends BNNII, showing how ground truth information, information regarding the particular parameter contour under reconstruction, and information regarding the underlying physical process, can be seamlessly added to the problem solution. 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 apply these Bayesian methods to a synthetic remote sensing problem, showing that the addition of ground truth information, which is naturally included through Bayesian modeling, provides a significant performance improvement.