  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.
