Julian Rasch

Julian Rasch, Eva-Maria Brinkmann, Martin Burger

Joint reconstruction has recently attracted a lot of attention, especially in the field of medical multi-modality imaging such as PET-MRI. Most of the developed methods rely on the comparison of image gradients, or more precisely their location, direction and magnitude, to make use of structural similarities between the images. A challenge and still an open issue for most of the methods is to handle images in entirely different scales, i.e. different magnitudes of gradients that cannot be dealt with by a global scaling of the data. We propose the use of generalized Bregman distances and infimal convolutions thereof with regard to the well-known total variation functional. The use of a total variation subgradient respectively the involved vector field rather than an image gradient naturally excludes the magnitudes of gradients, which in particular solves the scaling behavior. Additionally, the presented method features a weighting that allows to control the amount of interaction between channels. We give insights into the general behavior of the method, before we further tailor it to a particular application, namely PET-MRI joint reconstruction. To do so, we compute joint reconstruction results from blurry Poisson data for PET and undersampled Fourier data from MRI and show that we can gain a mutual benefit for both modalities. In particular, the results are superior to the respective separate reconstructions and other joint reconstruction methods.

Julian Rasch, Ville Kolehmainen, Riikka Nivajärvi et al.

The goal of dynamic magnetic resonance imaging (dynamic MRI) is to visualize tissue properties and their local changes over time that are traceable in the MR signal. We propose a new variational approach for the reconstruction of subsampled dynamic MR data, which combines smooth, temporal regularization with spatial total variation regularization. In particular, it furthermore uses the infimal convolution of two total variation Bregman distances to incorporate structural a-priori information from an anatomical MRI prescan into the reconstruction of the dynamic image sequence. The method promotes the reconstructed image sequence to have a high structural similarity to the anatomical prior, while still allowing for local intensity changes which are smooth in time. The approach is evaluated using artificial data simulating functional magnetic resonance imaging (fMRI), and experimental dynamic contrast-enhanced magnetic resonance data from small animal imaging using radial golden angle sampling of the k-space.

Julian Rasch, Florian Müller, Francesco Chiossi

Augmented Reality (AR) is transforming the way we interact with virtual information in the physical world. By overlaying digital content in real-world environments, AR enables new forms of immersive and engaging experiences. However, existing AR systems often struggle to effectively manage the many interactive possibilities that AR presents. This vision paper speculates on AI-driven approaches for adaptive AR content placement, dynamically adjusting to user movement and environmental changes. By leveraging machine learning methods, such a system would intelligently manage content distribution between AR projections integrated into the external environment and fixed static content, enabling seamless UI layout and potentially reducing users' cognitive load. By exploring the possibilities of AI-driven dynamic AR content placement, we aim to envision new opportunities for innovation and improvement in various industries, from urban navigation and workplace productivity to immersive learning and beyond. This paper outlines a vision for the development of more intuitive, engaging, and effective AI-powered AR experiences.

Julian Rasch, David Middelbeck

The goal of this paper is to introduce a new framework for fast and effective knowledge state assessments in the context of personalized, skill-based online learning. We use knowledge state networks - specific neural networks trained on assessment data of previous learners - to predict the full knowledge state of other learners from only partial information about their skills. In combination with a matching assessment strategy for asking discriminative questions we demonstrate that our approach leads to a significant speed-up of the assessment process - in terms of the necessary number of assessment questions - in comparison to standard assessment designs. In practice, the presented methods enable personalized, skill-based online learning also for skill ontologies of very fine granularity without deteriorating the associated learning experience by a lengthy assessment process.

Eva-Maria Brinkmann, Martin Burger, Julian Rasch et al.

The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on an appropriate set, the so-called model manifold. The latter is defined by Bregman distances or infimal convolutions thereof, using the (uniquely defined) subgradient appearing in the optimality condition of the variational method. For particular settings, such as anisotropic $\ell^1$ and TV-type regularization, previously used debiasing techniques are shown to be special cases. The proposed approach is however easily applicable to a wider range of regularizations. The two-step debiasing is shown to be well-defined and to optimally reduce bias in a certain setting. In addition to visual and PSNR-based evaluations, different notions of bias and variance decompositions are investigated in numerical studies. The improvements offered by the proposed scheme are demonstrated and its performance is shown to be comparable to optimal results obtained with Bregman iterations.