WIAS Preprint No. 3105, (2024)

Data--driven methods for quantitative imaging


Authors

  • Dong, Guozhi
    ORCID: 0000-0002-9674-6143
  • Flaschel, Moritz
    ORCID: 0000-0002-1365-9272
  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Papafitsoros, Kostas
    ORCID: 0000-0001-9691-4576
  • Sirotenko, Clemens
  • Tabelow, Karsten
    ORCID: 0000-0003-1274-9951

2020 Mathematics Subject Classification

  • 35R30 49J52 49K20 49M41 62G05 62G99 62P10 68T07 90C46

Keywords

  • Quantitative MRI, quantitative image reconstruction, regularization, variational methods, machine learning, neural networks, learning--informed physics

DOI

10.20347/WIAS.PREPRINT.3105

Abstract

In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly important in medical imaging applications, such as quantitative Magnetic Resonance Imaging (qMRI), where quantitative maps of biophysical parameters can characterize the imaged tissue and thus lead to more accurate diagnoses. Such quantitative values can also be useful in subsequent, automatized classification tasks in order to discriminate normal from abnormal tissue, for instance. The accurate reconstruction of these quantitative maps is typically achieved by solving two coupled inverse problems which involve a (forward) measurement operator, typically ill-posed, and a physical process that links the wanted quantitative parameters to the reconstructed qualitative image, given some underlying measurement data. In this review, by considering qMRI as a prototypical application, we provide a mathematically-oriented overview on how data-driven approaches can be employed in these inverse problems eventually improving the reconstruction of the associated quantitative maps.

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