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About this paper
Dominik Narnhofer, Andreas Habring, Martin Holler, Thomas Pock
Posterior variance is converted into calibrated, pixel-wise reconstruction-error bounds for imaging inverse problems. By applying conditional conformal calibration to Bayesian reconstructions, the framework achieves finite-sample coverage close to target levels across TV, Fields of Experts, and Total Deep Variation priors, as well as in accelerated MRI.
Key insights
- Conformal calibration separates coverage guarantees from the correctness of the Bayesian model: under exchangeability, approximate reconstructions and variance estimates can still yield valid error bounds.
- Posterior variance is informative about local reconstruction difficulty; higher uncertainty commonly corresponds to larger errors near edges, fine structures, and poorly observed regions.
- The quality and expressiveness of the prior affect tightness: learned FoE and TDV priors produce better reconstructions and generally narrower, more spatially meaningful bounds than TV.
Summary by alphaXiv.
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