Non-linear Optimization Methods for Quantitative Magnetic Resonance Imaging

Oliver Maier

Research output: ThesisDoctoral Thesis


Quantitative MRI (qMRI) offers objective parameters to describe the condition of tissue but is seldom used in clinical diagnostic. One substantial challenge for its use is the increased number of scans required to produce quantitative images, which leads to unacceptable scan time. The problem of increased scan time is especially pronounced in high resolution 3D imaging. Reducing the scan time causes a poor Signal-to-Noise Ratio (SNR) and can introduce artifacts in the final parameter maps. The goal of this work is to explore the
acceleration and noise removal potential of 3D spatial information between neighbouring voxels in parameter maps. The spatial information is extracted using finite differences in 3D and is joint over all parameter maps. The main assumption is that the spatial information is similar in different parameter maps, i.e. edges between different tissues in the individual parameter maps are located at the same position. Joining the information permits the separation of noise and artifacts from actual image content, enabling the reconstruction of high quality parameter maps from noisy and possibly undersampled data. These assumptions are used as regularization in an optimization approach and are paired with the Magnetic Resonance Imaging (MRI) forward operator, consisting of a non-linear signal description, coil sensitivity information and Fourier transformation with sampling. This combination allows parameter quantification directly from raw complex k-space data or from image data. The combination of regularization and the MRI forward operator is commonly referred to as model-based reconstruction. The proposed method was applied to different parameter mapping problems to show the general applicability of the approach, e.g. accelerated relaxometry using sparsely sampled data and noise suppression in perfusion imaging using arterial spin labeling. The developed approach was able to outperformed state-of-the-art reference methods in each of these applications, showing improved visual quality and quantitative accuracy. The improved quality from low SNR and accelerated data makes the proposed approach promising for important functional and microstructural imaging questions and opens the way for the adoption of qMRI as biomarker imaging
method for clinical routine applications.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Graz University of Technology (90000)
  • Stollberger, Rudolf, Supervisor
  • Kozerke, Sebastian, Supervisor, External person
Thesis sponsors
Award date29 Jun 2021
Publication statusPublished - 2021


  • MRI
  • relaxometry
  • model-based reconstruction
  • quantitative imaging


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