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@PHDTHESIS{Terhag:1024583,
      author       = {Terhag, Felix},
      othercontributors = {Tempone, Raul and Basermann, Achim and Kebaier, Ahmed},
      title        = {{S}tructure-exploiting uncertainty quantification and
                      control : {B}ayesian inference and {I}tô {SDE} methods from
                      {MRI} segmentation to autonomous sensing},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2026-00164},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2025},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University 2026; Dissertation, RWTH Aachen University, 2025},
      abstract     = {Uncertainty is a defining feature of both medical imaging
                      and autonomous decision-making. In clinical diagnostics,
                      inaccurate predictions can lead to harmful outcomes, while
                      in autonomous sensing, uncertainty in partial observations
                      can hinder safe and efficient control. This thesis develops
                      methods that both quantify uncertainty and exploit
                      problem-specific structure, demonstrating their
                      effectiveness across two distinct but connected domains. The
                      first part addresses challenges in cardiac magnetic
                      resonance imaging, where automated segmentation methods
                      often produce overconfident estimates of ventricular
                      volumes. A post-hoc uncertainty quantification method based
                      on Itô stochastic differential equations is introduced to
                      model prediction error dynamics; we establish the existence
                      of a unique strong solution that is non-negative almost
                      surely and prove that the procedure is bias-free with
                      respect to the underlying automatic segmentation. Moving
                      from classical cine MRI to real-time MRI, where thousands of
                      frames must be processed to capture both cardiac and
                      respiratory motion, the main challenge shifts from
                      overconfidence to the prohibitive cost of manual labeling.
                      To address this, we employ sparse Bayesian learning, to
                      automatically prune irrelevant frequency components,
                      leveraging the dominant frequency structure of heartbeat and
                      respiration to identify the most informative frames to
                      label. We show that the resulting greedy selection scheme
                      admits approximation guarantees relative to the optimal
                      scheme. Finally, spatial correlations between slices are
                      incorporated into the Bayesian framework, improving
                      predictive accuracy when labeled data are scarce. The second
                      part turns to multi-agent localization of an unknown
                      pollutant source under partial observation. We cast the
                      problem as a continuous–discrete stochastic control
                      system: between measurements, the value function evolves
                      according to Hamilton–Jacobi–Bellman dynamics, and at
                      observation times Gaussian Bayesian updates incorporate new
                      data. Directly solving the high-dimensional HJB equation is
                      computationally demanding, so we exploit structural
                      properties of the problem to improve efficiency. For
                      example, since the dominant uncertainty often aligns with
                      the wind direction, the discretization of the posterior can
                      be concentrated along this axis, reducing the number of grid
                      points required. Similarly, permutation symmetry across
                      agents allows a decomposition of the value function
                      analogous to analysis of variance, enabling scalable
                      approximations by retaining only single- and pairwise
                      interaction terms. This approach mitigates the curse of
                      dimensionality and provides flexibility, as objectives such
                      as collision avoidance or patrolling trajectories can be
                      incorporated seamlessly. This work combines Bayesian
                      inference and stochastic differential equations to address
                      challenges in cardiac imaging and autonomous sensing. By
                      exploiting inherent problem structure, it renders otherwise
                      intractable inference and control problems computationally
                      feasible, advancing both the theory and application of
                      uncertainty quantification and optimal decision-making.},
      cin          = {118110 / 110000},
      ddc          = {510},
      cid          = {$I:(DE-82)118110_20190107$ / $I:(DE-82)110000_20140620$},
      pnm          = {HDS LEE - Helmholtz School for Data Science in Life, Earth
                      and Energy (HDS LEE) (HDS-LEE-20190612) /
                      Doktorandenprogramm (PHD-PROGRAM-20170404)},
      pid          = {G:(DE-Juel1)HDS-LEE-20190612 /
                      G:(DE-HGF)PHD-PROGRAM-20170404},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2026-00164},
      url          = {https://publications.rwth-aachen.de/record/1024583},
}