Denoising Score-Matching for Uncertainty Quantification in Inverse Problems
This addresses uncertainty quantification for inverse problems like MRI reconstruction, but it is incremental as it builds on existing denoising score matching and Bayesian methods.
The authors tackled the problem of uncertainty quantification in inverse problems by proposing a Bayesian framework that uses denoising score matching to learn a prior and annealed Hamiltonian Monte-Carlo for posterior sampling, applied to MRI reconstruction to yield high-quality reconstructions and assess feature uncertainty.
Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework forsolving inverse problems, in which we limit the use of deep neural networks tolearning a prior distribution on the signals to recover. We adopt recent denoisingscore matching techniques to learn this prior from data, and subsequently use it aspart of an annealed Hamiltonian Monte-Carlo scheme to sample the full posteriorof image inverse problems. We apply this framework to Magnetic ResonanceImage (MRI) reconstruction and illustrate how this approach not only yields highquality reconstructions but can also be used to assess the uncertainty on particularfeatures of a reconstructed image.