arXiv subjects

Thorsten M. Buzug

Publications and source records attributed to Thorsten M. Buzug.

7 recordsLinked to original sources

arXiv2026

Unsupervised Deep Learning for Inverse Problems in Computed Tomography

Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available. To emulate this, in this study we assume it is unknown how to solve the imaging problem of Computed Tomography. We introduce an unsupervised deep learning framework that leverages the inherent similarities between iterative reconstruction, Deep Image Prior (DIP), and unrolled optimization schemes. Our specific contribution is a training framework for amortized reconstruction: After training on a dataset without any image-domain ground truth, reconstruction of an unseen scan reduces to a single network forward pass. We demonstrate the feasibility of reconstructing images from measurement data by pure network inference, without additional gradient steps for unseen samples. Our method is evaluated on the two-dimensional 2DeteCT dataset. Within a controlled, geometry-matched benchmark, our reconstructions are competitive with, or better than, filtered back-projection, maximum-likelihood reconstruction, and a supervised network of identical architecture. Compared to a per-image DIP baseline, our method reaches similar quality while replacing the costly per-instance optimization with a single forward pass, yielding a speed-up of about four orders of magnitude. This makes it a promising candidate for time-critical imaging applications. Future work will address multi-dataset adaptability, counter-measures against over-smoothing, advanced uncertainty quantification, and further medical-imaging inverse problems.

physics.med-ph↗

arXiv2026

Unsupervised Physics-Informed Deep Learning for Dual-Energy CT Material Decomposition

Dual-energy computed tomography (DECT) enables material-specific imaging through acquisitions at two different X-ray energy spectra. Material decomposition from DECT data is an ill-posed inverse problem that is highly sensitive to noise amplification. Conventional methods face challenges regarding accuracy and computational efficiency. We present a novel physics-informed deep learning (DL) framework for DECT material decomposition that eliminates the requirement for ground-truth material images during training. Our approach incorporates a polychromatic forward model into the training pipeline, enabling the network to learn the decomposition mapping by minimizing discrepancies in the projection domain. We validate our method on the AAPM DL-Spectral CT Challenge dataset, comparing performance against three state-of-the-art methods. In the projection domain, our method achieves the lowest root mean squared error (RMSE) across test datasets. For virtual monoenergetic images (VMIs) at 30 keV, 50 keV, and 70 keV, the approach consistently outperforms all conventional methods in both RMSE and structural similarity index (SSIM). These results demonstrate the potential of DL for accurate material decomposition in DECT without requiring labeled training data.

physics.med-ph↗

arXiv2023

Integrable Magnetic Fluid Hyperthermia Systems for 3D Magnetic Particle Imaging

Background: Combining magnetic particle imaging (MPI) and magnetic fluid hyperthermia (MFH) offers the ability to perform localized hyperthermia and magnetic particle imaging-assisted ther-mometry of hyperthermia treatment. This allows precise regional selective heating inside the body without invasive interventions. In current MPI-MFH platforms, separate systems are used, which require object transfer from one system to another. Here, we present the design, development and evaluation process for integrable MFH platforms, which extends a commercial MPI scanner with the functionality of MFH. Methods: The biggest issue of integrating magnetic fluid hyperthermia platforms into a magnetic par-ticle imaging system is the magnetic coupling of the devices, which induces high voltage in the imaging system, and is harming its components. In this paper we use a self-compensation approach derived from heuristic algorithms to protect the magnetic particle imaging scanner. The integrable platforms are evaluated regarding electrical and magnetic characteristics, cooling capability, field strength, the magnetic coupling to a replica of the magnetic particle imaging system's main solenoid and particle heating. Results: The MFH platforms generate suitable magnetic fields for magnetic heating of particles and are compatible with a commercial magnetic particle imaging scanner. In combination with the imaging system, selective heating with a gradient field and steerable heating positioning using the MPI focus fields are possible. Conclusion: The proposed MFH platforms serve as a therapeutic tool to unlock MFH functionality of a commercial magnetic particle imaging scanner, enabling its use in future preclinical trials of MPI-guided, spatially selective magnetic hyperthermia therapy.

physics.ins-det↗

arXiv2018

Moving Table Magnetic Particle Imaging: A stepwise approach preserving high spatio-temporal resolution

Magnetic Particle Imaging (MPI) is a highly sensitive imaging method that enables the visualization of magnetic tracer materials with a temporal resolution of more than 46 volumes per second. In MPI the size of the field of view scales with the strengths of the applied magnetic fields. In clinical applications those strengths are limited by peripheral nerve stimulation, specific absorption rates, and the requirement to acquire images of high spatial resolution. Therefore, the size of the field of view is usually a few cubic centimeters. To bypass this limitation, additional focus fields and/or external object movements can be applied. In this work, the latter approach is investigated. An object is moved through the scanner bore one step at a time, while the MPI scanner continuously acquires data from its static field of view. Using a 3D phantom and dynamic 3D in vivo data it is shown that the data from such a moving table experiment can be jointly reconstructed after reordering the data with respect to the stepwise object shifts and heart beat phases.

physics.med-ph↗

arXiv2017

Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging

Magnetic particle imaging (MPI) is a promising new in-vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

math.NA↗

arXiv2017

Towards Picogram Detection of Superparamagnetic Iron-Oxide Particles Using a Gradiometric Receive Coil

Superparamagnetic iron-oxide nanoparticles can be used in a variety of medical applications like vascular or targeted imaging. Magnetic particle imaging (MPI) is a promising tomographic imaging technique that allows visualizing the 3D nanoparticle distribution concentration in a non-invasive manner. The two main strengths of MPI are high temporal resolution and high sensitivity. While the first has been proven in the assessment of dynamic processes like cardiac imaging, it is unknown how far the detection limit of MPI can be lowered. Within this work, we will present a highly sensitive gradiometric receive-coil unit combined with a noise-matching network tailored for the measurement of mice. The setup is capable of detecting 5 ng of iron in vitro at 2.14 sec acquisition time. In terms of iron concentration we are able to detect 156 μg/L marking the lowest value that has been reported for an MPI scanner so far. In vivo MPI mouse images of a 512 ng bolus at 21.5 ms acquisition time allow for capturing the flow of an intravenously injected tracer through the heart of a mouse. Since it has been rather difficult to compare detection limits across MPI publications we propose guidelines improving the comparability of future MPI studies.

physics.med-ph↗

arXiv2014

Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves

Motivated by an application in Magnetic Particle Imaging, we study bivariate Lagrange interpolation at the node points of Lissajous curves. The resulting theory is a generalization of the polynomial interpolation theory developed for a node set known as Padua points. With appropriately defined polynomial spaces, we will show that the node points of non-degenerate Lissajous curves allow unique interpolation and can be used for quadrature rules in the bivariate setting. An explicit formula for the Lagrange polynomials allows to compute the interpolating polynomial with a simple algorithmic scheme. Compared to the already established schemes of the Padua and Xu points, the numerical results for the proposed scheme show similar approximation errors and a similar growth of the Lebesgue constant.

math.NA↗