A Probabilistic Deep Image Prior over Image Space

Riccardo Barbano, Javier Antoran, José Miguel Hernández-Lobato, Bangti Jin

Keywords: Image Reconstruction, Uncertainty Quantification, BNNs, Prior, Linearised, Laplace, Inverse Problems

TL;DR: We translate a function space prior into weight space and perform linearised Laplace inference in the deep image prior

Abstract: The deep image prior regularises under-specified image reconstruction problems by reparametrising the target image as the output of a CNN. We induce a prior over images by scoring CNN outputs using a classical image reconstruction regulariser. We translate this functional prior into weight space using a change of variables and propose an efficient linearised Laplace inference algorithm. Hyperparameters are optimised with Type-II MAP. We obtain pixel-wise uncertainty estimates, which we show to be calibrated to the reconstruction error.