Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction

• URL: http://arxiv.org/abs/2102.06665v1
• Date: Fri, 12 Feb 2021 18:08:14 GMT
• Title: Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction
• Authors: Dominik Narnhofer and Alexander Effland and Erich Kobler and Kerstin Hammernik and Florian Knoll and Thomas Pock
• Abstract summary: We introduce a Bayesian variational framework to quantify the model-immanent (epistemic) uncertainty. We demonstrate that our approach yields competitive results for undersampled MRI reconstruction.
• Score: 63.202627467245584
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.

Related papers

• With or Without Replacement? Improving Confidence in Fourier Imaging [5.542462410129539]
  We show how a transition between sampling with and without replacement can lead to a weighted reconstruction scheme with improved performance for the standard LASSO. In this paper, we illustrate how this reweighted sampling idea can also improve the debiased estimator.
  arXiv  Detail & Related papers  (2024-07-18T15:15:19Z)
• Deep Evidential Learning for Radiotherapy Dose Prediction [0.0]
  We present a novel application of an uncertainty-quantification framework called Deep Evidential Learning in the domain of radiotherapy dose prediction. We found that this model can be effectively harnessed to yield uncertainty estimates that inherited correlations with prediction errors upon completion of network training.
  arXiv  Detail & Related papers  (2024-04-26T02:43:45Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• PixCUE -- Joint Uncertainty Estimation and Image Reconstruction in MRI using Deep Pixel Classification [0.0]
  We introduce a method to estimate uncertainty during MRI reconstruction using a pixel classification framework. We demonstrate that this approach generates uncertainty maps that highly correlate with the reconstruction errors. We conclude that PixCUE is capable of reliably estimating the uncertainty in MRI reconstruction with a minimum additional computational cost.
  arXiv  Detail & Related papers  (2023-02-28T22:26:18Z)
• Model-Based Uncertainty in Value Functions [89.31922008981735]
  We focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty Bellman equation. We propose a new uncertainty Bellman equation whose solution converges to the true posterior variance over values.
  arXiv  Detail & Related papers  (2023-02-24T09:18:27Z)
• Trustworthy Multimodal Regression with Mixture of Normal-inverse Gamma Distributions [91.63716984911278]
  We introduce a novel Mixture of Normal-Inverse Gamma distributions (MoNIG) algorithm, which efficiently estimates uncertainty in principle for adaptive integration of different modalities and produces a trustworthy regression result. Experimental results on both synthetic and different real-world data demonstrate the effectiveness and trustworthiness of our method on various multimodal regression tasks.
  arXiv  Detail & Related papers  (2021-11-11T14:28:12Z)
• The role of MRI physics in brain segmentation CNNs: achieving acquisition invariance and instructive uncertainties [3.46329153611365]
  In this paper we demonstrate the efficacy of a physics-informed, uncertainty-aware, segmentation network. We show that the proposed approach also accurately extrapolates to out-of-distribution sequence samples. We demonstrate a significant improvement in terms of coefficients of variation, backed by uncertainty based volumetric validation.
  arXiv  Detail & Related papers  (2021-11-04T11:52:49Z)
• Deep Quantile Regression for Uncertainty Estimation in Unsupervised and Supervised Lesion Detection [0.0]
  Uncertainty is important in critical applications such as anomaly or lesion detection and clinical diagnosis. In this work, we focus on using quantile regression to estimate aleatoric uncertainty and use it for estimating uncertainty in both supervised and unsupervised lesion detection problems. We show how quantile regression can be used to characterize expert disagreement in the location of lesion boundaries.
  arXiv  Detail & Related papers  (2021-09-20T08:50:21Z)
• The Risks of Invariant Risk Minimization [52.7137956951533]
  Invariant Risk Minimization is an objective based on the idea for learning deep, invariant features of data. We present the first analysis of classification under the IRM objective--as well as these recently proposed alternatives--under a fairly natural and general model. We show that IRM can fail catastrophically unless the test data are sufficiently similar to the training distribution--this is precisely the issue that it was intended to solve.
  arXiv  Detail & Related papers  (2020-10-12T14:54:32Z)
• Learning to Predict Error for MRI Reconstruction [67.76632988696943]
  We demonstrate that predictive uncertainty estimated by the current methods does not highly correlate with prediction error. We propose a novel method that estimates the target labels and magnitude of the prediction error in two steps.
  arXiv  Detail & Related papers  (2020-02-13T15:55:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.