A Probabilistic Deep Image Prior for Computational Tomography

• URL: http://arxiv.org/abs/2203.00479v1
• Date: Mon, 28 Feb 2022 14:47:14 GMT
• Title: A Probabilistic Deep Image Prior for Computational Tomography
• Authors: Javier Antor\'an, Riccardo Barbano, Johannes Leuschner, Jos\'e Miguel Hern\'andez-Lobato, Bangti Jin
• Abstract summary: Existing deep-learning based tomographic image reconstruction methods do not provide accurate estimates of reconstruction uncertainty. We construct a Bayesian prior for tomographic reconstruction, which combines the classical total variation (TV) regulariser with the modern deep image prior (DIP) For the inference, we develop an approach based on the linearised Laplace method, which is scalable to high-dimensional settings.
• Score: 0.19573380763700707
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Existing deep-learning based tomographic image reconstruction methods do not provide accurate estimates of reconstruction uncertainty, hindering their real-world deployment. To address this limitation, we construct a Bayesian prior for tomographic reconstruction, which combines the classical total variation (TV) regulariser with the modern deep image prior (DIP). Specifically, we use a change of variables to connect our prior beliefs on the image TV semi-norm with the hyper-parameters of the DIP network. For the inference, we develop an approach based on the linearised Laplace method, which is scalable to high-dimensional settings. The resulting framework provides pixel-wise uncertainty estimates and a marginal likelihood objective for hyperparameter optimisation. We demonstrate the method on synthetic and real-measured high-resolution $\mu$CT data, and show that it provides superior calibration of uncertainty estimates relative to previous probabilistic formulations of the DIP.

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