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Quantifying Model Uncertainty in Inverse Problems via Bayesian Deep Gradient Descent

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Document pages: 8 pages

Abstract: Recent advances in reconstruction methods for inverse problems leveragepowerful data-driven models, e.g., deep neural networks. These techniques havedemonstrated state-of-the-art performances for several imaging tasks, but theyoften do not provide uncertainty on the obtained reconstruction. In this work,we develop a scalable, data-driven, knowledge-aided computational framework toquantify the model uncertainty via Bayesian neural networks. The approachbuilds on, and extends deep gradient descent, a recently developed greedyiterative training scheme, and recasts it within a probabilistic framework.Scalability is achieved by being hybrid in the architecture: only the lastlayer of each block is Bayesian, while the others remain deterministic, and bybeing greedy in training. The framework is showcased on one representativemedical imaging modality, viz. computed tomography with either sparse view orlimited view data, and exhibits competitive performance with respect tostate-of-the-art benchmarks, e.g., total variation, deep gradient descent andlearned primal-dual.

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