A Variational Inference Framework for Inverse Problems

We present a framework for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy performances and reduced model fitting times, when compared with standard Markov chain Monte Carlo methods. The message passing and factor graph fragment approach to variational Bayes we describe facilitates streamlined implementation of approximate inference algorithms and forms the basis to software development. Such approach allows for supple inclusion of numerous response distributions and penalizations into the inverse problem model. Albeit our analysis is circumscribed to one- and two-dimensional response variables, we lay down an infrastructure where streamlining algorithmic steps based on nullifying weak interactions between variables are extendible to inverse problems in higher dimensions. Image processing applications motivated by biomedical and archaeological problems are included as illustrations.