arXiv subjects

Matthias Günther

Publications and source records attributed to Matthias Günther.

5 recordsLinked to original sources

arXiv2026

Slice-Profile-Enabled Phase Distribution Graphs for MRI Simulation

MRI simulation often separates two descriptions that are both essential for realistic sequence analysis: Bloch dynamics for waveform-resolved radiofrequency (RF) excitation, and phase-graph methods for coherence-pathway evolution. Extended Phase Graph (EPG) models provide pathway tracking, and Phase--Distribution Graphs (PDG) extend this idea to spatially resolved $k$-space simulation, but existing PDG formulations rely on hard-pulse RF mixing that is \emph{order-local}: the RF pulse mixes $F_n^+$, $F_n^-$, and $Z_n$ at a fixed coherence order $n$, without coupling different $k_z$ orders. This work introduces a unified Bloch-resolved PDG framework for slice-profile-aware MRI simulation. A scanner-rasterized sequence is partitioned into RF-sensitive Bloch spans and non-RF phase-graph spans. For each unique RF span, Bloch dynamics are solved on a slice grid to obtain a spatially varying propagator $R(z)$. Its Fourier coefficients $\mathcal{R}_Δ$, indexed by slice-order offset $Δ$, are compiled into the PDG state graph as sparse cross-order coupling in $k_z$. Graph growth is controlled by retaining the dominant Fourier coefficients and pruning low-contribution PDG states. This retains PDG pathway history and voxel-wise image formation while incorporating shaped slice-selective and off-resonant RF behavior. Experiments show close agreement with direct one-dimensional Bloch slice-profile evolution through repeated excitations, while retaining only a few hundred active PDG states. Image simulations further illustrate slice-position dependence, fat-suppression behavior, measured three-dimensional $B_0$ field maps, and comparison with scanner data. The proposed framework enables sequence-consistent simulation and signal formation understanding in regimes where RF physics, spatial encoding, object heterogeneity, and echo-pathway formation interact.

physics.med-ph↗

arXiv2026

Multimodal synthesis of MRI and tabular data with diffusion in a joint latent space via cross-attention

We propose a multimodal latent diffusion model that jointly synthesizes volumetric magnetic resonance imaging (MRI) and tabular clinical data within a shared latent space via cross-attention. This approach enables coherent joint representation learning of MRI and tabular modalities for generative modeling. Our model utilizes a variational autoencoder to fuse the two modalities before diffusion-based synthesis, allowing modality-appropriate reconstruction with separate decoders for MRI and tabular data. We evaluated the framework on data from the German National Cohort (NAKO Gesundheitsstudie), comprising over 10,000 participants with MRI scans and clinical tabular features such as age, sex, body measurements, and ethnicity. The generated MRI volumes exhibited anatomical plausibility and body composition consistent with the synthesized tabular attributes. Quantitative evaluation using Fréchet distance and precision-recall metrics confirmed high-fidelity image generation. In the tabular modality, our model outperformed CTGAN across standard evaluation metrics and achieved results comparable to TVAE, demonstrating competitive performance relative to established unimodal baselines. This work is, to our knowledge, the first to demonstrate the feasibility of jointly modeling MRI and mixed-type tabular data in a single latent diffusion framework, offering a proof-of-concept for generating coherent synthetic multimodal patient data and aligning with the broader goal of developing digital twins in healthcare.

eess.IV↗

arXiv2026

Remarks on infimum and maximal lower bounds of a set of bounded self-adjoint operators

The notions of infimum and maximal lower bounds of a set $\mathfrak M$ of bounded self-adjoint operators were mainly studied for a set $\mathfrak M$ of two elements. The present paper deals with more general sets $\mathfrak M$, where it is required that $\mathfrak M$ is nonempty and bounded from below. Kadison's theorem on the existence of the infimum of a two-element set is proved for a countable and weak-operator compact set $\mathfrak M$. Stott's recent results on the structure of the set of maximal lower bounds of a finite set of Hermitian matrices are discussed and partially generalized. We are also concerned with the greatest lower bound and maximal lower bounds under certain restrictions. It is shown that the set of all lower bounds of $\mathfrak M$ commuting with all elements of $\mathfrak M$ possesses the greatest element if $\mathfrak M$ is a set of pairwise commuting operators. The theorem of Moreland and Gudder on the existence of the greatest positive lower bound of a set of two positive matrices is extended to an arbitrary finite set of positive matrices.

math.FA↗

arXiv2025

Differentiable Simulator for Electrically Reconfigurable Electromagnetic Structures

This paper introduces a novel CUDA-enabled PyTorch-based framework designed for the gradient-based optimization of such reconfigurable electromagnetic structures with electrically tunable parameters. Traditional optimization techniques for these structures often rely on non-gradient-based methods, limiting efficiency and flexibility. Our framework leverages automatic differentiation, facilitating the application of gradient-based optimization methods. This approach is particularly advantageous for embedding within deep learning frameworks, enabling sophisticated optimization strategies. We demonstrate the framework's effectiveness through comprehensive simulations involving resonant structures with tunable parameters. Key contributions include the efficient solution of the inverse problem. The framework's performance is validated using three different resonant structures: a single-loop copper wire (Unit-Cell) as well as an 8x1 and an 8x8 array of resonant unit cells with multiple inductively coupled unit cells (1d and 2d Metasurfaces). Results show precise in-silico control over the magnetic field's component normal to the surface of each resonant structure, achieving desired field strengths with minimal error. The proposed framework is compatible with existing simulation software. This PyTorch-based framework sets the stage for advanced electromagnetic control strategies for resonant structures with application in e.g. MRI, providing a robust platform for further exploration and innovation in the design and optimization of resonant electromagnetic structures.

physics.comp-ph↗

arXiv2023

Model-based Analysis and Specification of Functional Requirements and Tests for Complex Automotive Systems

The specification of requirements and tests are crucial activities in automotive development projects. However, due to the increasing complexity of automotive systems, practitioners fail to specify requirements and tests for distributed and evolving systems with complex interactions when following traditional development processes. To address this research gap, we propose a technique that starts with the early identification of validation concerns from a stakeholder perspective, which we use to systematically design tests that drive a scenario-based modeling and analysis of system requirements. To ensure complete and consistent requirements and test specifications in a form that is required in automotive development projects, we develop a Model-Based Systems Engineering (MBSE) methodology. This methodology supports system architects and test designers in the collaborative application of our technique and in maintaining a central system model, in order to automatically derive the required specifications. We evaluate our methodology by applying it at KOSTAL (Tier1 supplier) and within student projects as part of the masters program Embedded Systems Engineering. Our study corroborates that our methodology is applicable and improves existing requirements and test specification processes by supporting the integrated and stakeholder-focused modeling of product and validation systems, where the early definition of stakeholder and validation concerns fosters a problem-oriented, iterative and test-driven requirements modeling.

cs.SE↗