Variational Reformulation of Bayesian Inverse Problems
This work addresses computational bottlenecks in Bayesian inverse problems for researchers and practitioners in fields like geophysics or imaging, though it appears incremental as it builds on existing optimization and Bayesian frameworks.
The authors tackled the computational inefficiency of Bayesian inference for inverse problems by reformulating it as an optimization problem using information theory, resulting in a method that maintains theoretical soundness while improving computational efficiency.
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge, etc. The Bayesian formalism to inverse problems avoids most of the difficulties encountered by the optimization approach, albeit at an increased computational cost. In this work, we use information theoretic arguments to cast the Bayesian inference problem in terms of an optimization problem. The resulting scheme combines the theoretical soundness of fully Bayesian inference with the computational efficiency of a simple optimization.