The Weak Constraint Formulation of Bayesian Inverse Problems

Inverse problems arise in many applications. One could solve them by adopting a Bayesian framework, to account for uncertainty which arises from our observations. The solution of an inverse problem is given by a probability distribution. Usually, efficient methods at hand to extract information from this probability distribution involves the solution of an optimization problem, where the objective function is highly nonconvex. In this talk, we explore a reformulation of inverse problems, which helps in convexifying the objective function. We also discuss a method to sample from this probability distribution.