A variational inference framework for inverse problems
This work provides a more efficient and flexible method for researchers and practitioners dealing with inverse problems in fields like image processing and biomedicine, though it appears incremental as it builds on existing variational Bayes techniques.
The authors tackled the challenge of fitting inverse problem models by introducing a variational Bayes framework that ensures flexibility, accuracy, and reduced fitting times. In an image processing application and biomedical simulation, this approach demonstrated computational advantages over Markov chain Monte Carlo methods.
A framework is presented 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 and reduced model fitting times. The message passing and factor graph fragment approach to variational Bayes that is also described facilitates streamlined implementation of approximate inference algorithms and allows for supple inclusion of numerous response distributions and penalizations into the inverse problem model. Models for one- and two-dimensional response variables are examined and an infrastructure is laid down where efficient algorithm updates based on nullifying weak interactions between variables can also be derived for inverse problems in higher dimensions. An image processing application and a simulation exercise motivated by biomedical problems reveal the computational advantage offered by efficient implementation of variational Bayes over Markov chain Monte Carlo.