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Conference Papers Year : 2020

Denoising Score-Matching for Uncertainty Quantification in Inverse Problems

Abstract

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.
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Dates and versions

hal-03020167 , version 1 (23-11-2020)

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Zaccharie Ramzi, Benjamin Rémy, Francois Lanusse, Jean-Luc Starck, Philippe Ciuciu. Denoising Score-Matching for Uncertainty Quantification in Inverse Problems. NeurIPS 2020 - 34th Conference on Neural Information Processing Systems / Workshop on Deep Learning and Inverse Problems, Dec 2020, Vancouver / Virtuel, Canada. ⟨hal-03020167⟩
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