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Predictive uncertainty in deep learning-based MR image reconstruction using deep ensembles: Evaluation on the fastMRI

Thomas Küstner1, Kerstin Hammernik2,3, Daniel Rueckert2,3,4

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Summary

This study introduces a method to predict uncertainty in deep learning-based MR image reconstruction, improving robustness and detecting errors. The approach quantifies both data and model uncertainties for better diagnostic reliability.

Keywords:
MRIdeep ensemblesdeep learningepistemic and aleatoric uncertaintyimage reconstructionuncertainty estimation

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Area of Science:

  • Medical Imaging
  • Artificial Intelligence
  • Machine Learning

Background:

  • Deep learning (DL) models for MR image reconstruction risk generating unrealistic artifacts or missing pathologies.
  • Current DL methods are often task-agnostic and not robust to domain shifts, potentially leading to undetected errors.
  • Quantifying uncertainty in DL reconstructions is crucial for assessing robustness and reliability.

Purpose of the Study:

  • To develop and evaluate a method for pixel-wise predictive uncertainty estimation in DL-based MR image reconstruction.
  • To investigate the impact of domain shifts and varying network architectures on reconstruction uncertainty.
  • To differentiate between aleatoric (data) and epistemic (model) uncertainty.

Main Methods:

  • Proposed a strategy combining deep ensembles for epistemic uncertainty and nonnegative log-likelihood loss for aleatoric uncertainty.
  • Integrated this uncertainty estimation with conventional loss terms for DL reconstruction.
  • Evaluated five different DL architectures on the fastMRI database, testing with in-distributional and out-of-distributional data (varying undersampling, contrast, orientation, anatomy, pathology).

Main Results:

  • The proposed uncertainty measure effectively captured pixel-wise predictive uncertainty, correlating well with normalized mean squared error.
  • Uncertainty was localized to aliased anatomies and regions with abnormal signal intensity (hyper/hypointense).
  • The method successfully detected shifts in disease prevalence and revealed distinct uncertainty patterns across different network architectures.

Conclusions:

  • The developed approach enables robust estimation of both aleatoric and epistemic uncertainty in DL-based MR reconstruction.
  • Provides an interpretable, pixel-level examination of predictive uncertainty, enhancing model reliability.
  • Facilitates a deeper understanding of DL model behavior under various conditions and potential domain shifts.