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Item type:Publication, Access status: without files , Posterior temperature optimized Bayesian models for inverse problems in medical imagingWe present Posterior Temperature Optimized Bayesian Inverse Models (POTOBIM), an unsupervised Bayesian approach to inverse problems in medical imaging using mean-field variational inference with a fully tempered posterior. Bayesian methods exhibit useful properties for approaching inverse tasks, such as tomographic reconstruction or image denoising. A suitable prior distribution introduces regularization, which is needed to solve the ill-posed problem and reduces overfitting the data. In practice, however, this often results in a suboptimal posterior temperature, and the full potential of the Bayesian approach is not being exploited. In POTOBIM, we optimize both the parameters of the prior distribution and the posterior temperature with respect to reconstruction accuracy using Bayesian optimization with Gaussian process regression. Our method is extensively evaluated on four different inverse tasks on a variety of modalities with images from public data sets and we demonstrate that an optimized posterior temperature outperforms both non-Bayesian and Bayesian approaches without temperature optimization. The use of an optimized prior distribution and posterior temperature leads to improved accuracy and uncertainty estimation and we show that it is sufficient to find these hyperparameters per task domain. Well-tempered posteriors yield calibrated uncertainty, which increases the reliability in the predictions. Our source code is publicly available at github.com/Cardio-AI/mfvi-dip-mia.Publicationtype: Journal ArticleScopus© Citations 4 28 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A mean-field variational inference approach to deep image prior for inverse problems in medical imagingExploiting the deep image prior property of convolutional auto-encoder networks is especially interesting for medical image processing as it avoids hallucinations by omitting supervised learning. Its spectral bias towards lower frequencies makes it suitable for inverse image problems such as denoising and super-resolution, but manual early stopping has to be applied to act as a low-pass filter. In this paper, we present a novel Bayesian approach to deep image prior using mean-field variational inference. This allows for uncertainty quantification on a per-pixel level and, given the right prior distribution on the network weights, omits the need for early stopping. We optimize the parameters of the weight prior towards reconstruction accuracy using Bayesian optimization with Gaussian Process regression. We evaluate our approach on different inverse tasks on a variety of modalities and demonstrate that an optimized weight prior outperforms former state-of-the-art Bayesian deep image prior approaches. We show that a badly selected prior leads to worse accuracy and calibration and that it is sufficient to optimize the weight prior parameter per task domain.Publicationtype: Conference Paper15