The goal of MRI reconstruction is to restore a high fidelity image from partially observed measurements. This partial view naturally induces reconstruction uncertainty that can only be reduced by acquiring additional measurements. In this paper, we present a novel method for MRI reconstruction that, at inference time, dynamically selects the measurements to take and iteratively refines the prediction in order to best reduce the reconstruction error and, thus, its uncertainty. We validate our method on a large scale knee MRI dataset, as well as on ImageNet. Results show that (1) our system successfully outperforms active acquisition baselines; (2) our uncertainty estimates correlate with error maps; and (3) our ResNet-based architecture surpasses standard pixel-to-pixel models in the task of MRI reconstruction. The proposed method not only shows high-quality reconstructions but also paves the road towards more applicable solutions for accelerating MRI.
Significant effort has been devoted in the computer vision literature to provide uncertainty estimates @cite_35 of predictions. There are two possible sources of uncertainty @cite_7 : 1) model uncertainty due to an imperfect model (epistemic uncertainty) and 2) data uncertainty due to imperfect measurements (aleatoric uncertainty). While model uncertainty can be decreased with better models, data uncertainty vanishes only with the observation of all variables with infinite precision. In medical imaging, uncertainty is often used to display probable errors @cite_42 and has been mainly studied in the context of image segmentation @cite_15 @cite_19 . Segmentation errors (i.e. wrong label predictions) are often easier to detect by domain experts than reconstruction errors (i.e. shift of pixel values), which could potentially mislead diagnosis. Therefore, the study of uncertainty is crucial in the context of MRI reconstruction. In this paper, we focus on , which is caused by the partially observed -space. This uncertainty can be captured by proper model parametrization, e.g. in regression tasks a Gaussian observation model is often assumed @cite_35 @cite_50 ; this assumption can be relaxed to allow the use of arbitrary observation models as explained in @cite_57 .
@cite_35 @cite_7 @cite_42 @cite_57 @cite_19 @cite_50 @cite_15
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There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model - uncertainty which can be explained away given enough data. Traditionally it has been difficult to model epistemic uncertainty in computer vision, but with new Bayesian deep learning tools this is now possible. We study the benefits of modeling epistemic vs. aleatoric uncertainty in Bayesian deep learning models for vision tasks. For this we present a Bayesian deep learning framework combining input-dependent aleatoric uncertainty together with epistemic uncertainty. We study models under the framework with per-pixel semantic segmentation and depth regression tasks. Further, our explicit uncertainty formulation leads to new loss functions for these tasks, which can be interpreted as learned attenuation. This makes the loss more robust to noisy data, also giving new state-of-the-art results on segmentation and depth regression benchmarks. There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained away given enough data. Traditionally it has been difficult to model epistemic uncertainty in computer vision, but with new Bayesian deep learning tools this is now possible. We study the benefits of modeling epistemic vs. aleatoric uncertainty in Bayesian deep learning models for vision tasks. For this we present a Bayesian deep learning framework combining input-dependent aleatoric uncertainty together with epistemic uncertainty. We study models under the framework with per-pixel semantic segmentation and depth regression tasks. Further, our explicit uncertainty formulation leads to new loss functions for these tasks, which can be interpreted as learned attenuation. This makes the loss more robust to noisy data, also giving new state-of-the-art results on segmentation and depth regression benchmarks. Deep learning (DL) has revolutionized the field of computer vision and image processing. In medical imaging, algorithmic solutions based on DL have been shown to achieve high performance on tasks that previously required medical experts. However, DL-based solutions for disease detection have been proposed without methods to quantify and control their uncertainty in a decision. In contrast, a physician knows whether she is uncertain about a case and will consult more experienced colleagues if needed. Here we evaluate drop-out based Bayesian uncertainty measures for DL in diagnosing diabetic retinopathy (DR) from fundus images and show that it captures uncertainty better than straightforward alternatives. Furthermore, we show that uncertainty informed decision referral can improve diagnostic performance. Experiments across different networks, tasks and datasets show robust generalization. Depending on network capacity and task dataset difficulty, we surpass 85 sensitivity and 80 specificity as recommended by the NHS when referring 0−20 of the most uncertain decisions for further inspection. We analyse causes of uncertainty by relating intuitions from 2D visualizations to the high-dimensional image space. While uncertainty is sensitive to clinically relevant cases, sensitivity to unfamiliar data samples is task dependent, but can be rendered more robust. Uncertainty estimates of modern neuronal networks provide additional information next to the computed predictions and are thus expected to improve the understanding of the underlying model. Reliable uncertainties are particularly interesting for safety-critical computer-assisted applications in medicine, e.g., neurosurgical interventions and radiotherapy planning. We propose an uncertainty-driven sanity check for the identification of segmentation results that need particular expert review. Our method uses a fully-convolutional neural network and computes uncertainty estimates by the principle of Monte Carlo dropout. We evaluate the performance of the proposed method on a clinical dataset with 30 postoperative brain tumor images. The method can segment the highly inhomogeneous resection cavities accurately (Dice coefficients 0.792 @math 0.154). Furthermore, the proposed sanity check is able to detect the worst segmentation and three out of the four outliers. The results highlight the potential of using the additional information from the model's parameter uncertainty to validate the segmentation performance of a deep learning model.