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Imaging with Confidence: Uncertainty Quantification for High-Dimensional Undersampled MR Images

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Computer Vision – ECCV 2024 (ECCV 2024)

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Abstract

Establishing certified uncertainty quantification (UQ) in imaging processing applications continues to pose a significant challenge. In particular, such a goal is crucial for accurate and reliable medical imaging if one aims for precise diagnostics and appropriate intervention. In the case of magnetic resonance imaging, one of the essential tools of modern medicine, enormous advancements in fast image acquisition were possible after the introduction of compressive sensing and, more recently, deep learning methods. Still, as of now, there is no UQ method that is both fully rigorous and scalable. This work takes a step towards closing this gap by proposing a total variation minimization-based method for pixel-wise sharp confidence intervals for undersampled MRI. We demonstrate that our method empirically achieves the predicted confidence levels. We expect that our approach will also have implications for other imaging modalities as well as deep learning applications in computer vision. Our code is available on GitHub https://github.com/HannahLaus/Project_UQ_TV.git.

F. Hoppe, C. M. Verdun, and H. Laus—These authors contributed equally to this work.

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Notes

  1. 1.

    The notation m(N) considers a sequence of regression problems, where both dimensions m and N are growing with the rate \(\frac{s\sqrt{\log N}}{m}\rightarrow 0\).

  2. 2.

    https://github.com/HannahLaus/Project_UQ_TV.git.

  3. 3.

    Siemens Healthineers, Erlangen, Germany.

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Acknowledgments

We gratefully acknowledge financial support with funds provided by the German Federal Ministry of Education and Research in the grant “SparseMRI3D+: Compressive Sensing und Quantifizierung von Unsicherheiten für die beschleunigte multiparametrische quantitative Magnetresonanztomografie (FZK 05M20WOA)” and funding by the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreement No. 952172.

Author information

Authors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Frederik Hoppe

  2. Harvard University, Cambridge, USA

    Claudio Mayrink Verdun

  3. TU Munich and MCML, Munich, Germany

    Hannah Laus & Felix Krahmer

  4. TH Ingolstadt, TU Munich and GE HealthCare, Munich, Germany

    Sebastian Endt & Marion I. Menzel

  5. LMU Munich and MCML, Munich, Germany

    Holger Rauhut

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  1. Frederik Hoppe
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Correspondence to Frederik Hoppe .

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Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Aleš Leonardis

  2. University of Trento, Trento, Italy

    Elisa Ricci

  3. Technical University of Darmstadt, Darmstadt, Hessen, Germany

    Stefan Roth

  4. Princeton University, Palo Alto, CA, USA

    Olga Russakovsky

  5. Czech Technical University in Prague, Prague, Czech Republic

    Torsten Sattler

  6. École des Ponts ParisTech, Marne-la-Vallée, France

    Gül Varol

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Hoppe, F. et al. (2025). Imaging with Confidence: Uncertainty Quantification for High-Dimensional Undersampled MR Images. In: Leonardis, A., Ricci, E., Roth, S., Russakovsky, O., Sattler, T., Varol, G. (eds) Computer Vision – ECCV 2024. ECCV 2024. Lecture Notes in Computer Science, vol 15136. Springer, Cham. https://doi.org/10.1007/978-3-031-73229-4_25

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