arXiv subjects

Vladyslav Gapyak

Publications and source records attributed to Vladyslav Gapyak.

7 recordsLinked to original sources

arXiv2026

MPISuperRes-PnP: A Super-Resolution Zero-Shot Plug-and-Play Reconstruction Algorithm for Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is an emerging medical imaging modality. MPI is based on the non-linear response of magnetic nanoparticles to an applied magnetic field and avoids ionizing radiation. The measured signal is the voltage induced in receive coils by the particles' response. Reconstructing the particle concentration from the signal constitutes the imaging task. Even using state-of-the-art measurement-based reconstruction, the associated spatial grid is very coarse, hence super-resolution (SR) techniques are important. In this work, we propose an approach for SR in MPI inspired by energy minimization. Different methods have been proposed for SR in MPI, ranging from upscaling of the associated system matrix to interpolation of the reconstruction. Here we incorporate SR into the reconstruction task via an energy minimization formulation. Following the plug-and-play approach to energy minimization we derive a splitting scheme and a SR method for MPI where the arising Gaussian denoising task is treated with a pre-trained learned Gaussian denoiser in a zero-shot fashion. This way, we incorporate benefits of deep learning without training and avoid the need of training data. Further, we provide a quantitative and qualitative evaluation of the proposed method. Hyper-parameter are selected via an extended parameter search. The found parameters are applied for reconstruction on real data. We show the applicability of our method on synthetic and on real data (MPIData: EquilibriumModelWithAnisotropy and 2D-OpenMPI Data). The proposed method employs a deep-learning denoiser without training -- thus it does not require presently scarcely available MPI training data. The denoiser behaves conservatively, i.e., no hallucination artifacts were observed. The SR approach is generic such that it can be applied in future MPI contexts involving different regularizers or different imaging tasks.

cs.CV↗

arXiv2026

Debye Relaxation in Model-Based Multi-Dimensional Magnetic Particle Imaging

Model-based reconstruction approaches for the medical imaging modality Magnetic Particle Imaging (MPI) are typically based on the Langevin model, which assumes instantaneous alignment of the particles magnetic momenta with the applied field. Regarding the application to real data, Langevin model-based reconstruction methods require model transfer functions (MTF) obtained from calibrations to preprocess the data. There are also model-based reconstruction approaches that include relaxation effects and other particle-level dynamics. However, they are limited either to 1D or 1D-like scanning scenarios when considering real data, or are limited to simulated data in the case of multi-dimensional field-free point (FFP) MPI. Thus, fully model-based reconstructions from multi-dimensional FFP scanning data that incorporate relaxation effects without using an MTF have not yet been demonstrated. In this work, we incorporate relaxation effects by considering a multi-dimensional Debye model and provide reconstruction formulae. In particular, we show that the Debye model-based signal is the response of a linear time-invariant system with exponential memory applied to a Langevin model-based signal. We provide a reconstruction algorithm for the introduced multi-dimensional Debye model. To this end, we devise a relaxation adaption step. For the resulting relaxation-adapted Debye signal, we show that it can be expressed by the well-studied MPI core operator derived from the Langevin theory. This results in a three-stage algorithm with low additional cost over the Langevin model, as the relaxation adaption scales linearly in the input data. We provide numerical results for the proposed algorithmic approach. In particular, we obtain fully model-based reconstructions from real 2D MPI data without involving any specific MTF analogous to the Langevin model case.

math.NA↗

arXiv2025

Higher Order Regularization using Harmonic Eigenfunctions for Model-Based Reconstruction in Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is a recent imaging modality where superparamagnetic nanoparticles are employed as tracers. The reconstruction task is to obtain the spatial particle distribution from a voltage signal induced by the particles. Generally, in computational imaging variational reconstruction techniques are common and rely on a mathematical model to describe the underlying physics. For the MPI reconstruction task we propose a model-based variational reconstruction technique which incorporates a higher order regularizer, where the regularizer is diagonalized by harmonic eigenfunctions. The proposed image reconstruction algorithm features two major stages: in the first stage, the core stage, the components of the MPI core response are reconstructed. This is the MPI-specific data approximation task which we formulate as a variational problem incorporating the higher order regularizer. The relationship between the particle distribution, the MPI core response and the measured data is given by a mathematical model which was introduced in our earlier research. According to this model the MPI core response is tied to the particle distribution by convolution. Therefore the outcome of the core stage yields the data for the second stage, the deconvolution stage, in which the final reconstructed image is produced by solving an ill-posed deconvolution problem in a robust way relying on earlier research. Interestingly, the quality of the final image depends significantly on the quality of the result of the core stage. A contribution is thus the enhancement of the core stage via higher order regularization. We provide a theoretical foundation for our approach and demonstrate its benefit with numerical examples.

math.NA↗

arXiv2025

Reconstruction Formulae for 3D Field-Free Line Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is a promising noninvasive in vivo imaging modality that makes it possible to map the spatial distribution of superparamagnetic nanoparticles by exposing them to dynamic magnetic fields. In the Field-Free Line (FFL) scanner topology, the spatial encoding of the particle distribution is performed by applying magnetic fields vanishing on straight lines. The voltage induced in the receiving coils by the particles when exposed to the magnetic fields constitute the signal from which the particle distribution is to be reconstructed. To avoid lengthy calibration, model-based reconstruction formulae have been developed for the 2D FFL scanning topology. In this work we develop reconstruction formulae for 3D FFL. Moreover, we provide a model-based reconstruction algorithm for 3D FFL and we validate it with a numerical experiment.

math.NA↗

arXiv2025

Fast Trajectory-Independent Model-Based Reconstruction Algorithm for Multi-Dimensional Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is a promising tomographic technique for visualizing the spatio-temporal distribution of superparamagnetic nanoparticles, with applications ranging from cancer detection to real-time cardiovascular monitoring. Traditional MPI reconstruction relies on either time-consuming calibration (measured system matrix) or model-based simulation of the forward operator. Recent developments have shown the applicability of Chebyshev polynomials to multi-dimensional Lissajous Field-Free Point (FFP) scans. This method is bound to the particular choice of sinusoidal scanning trajectories. In this paper, we present the first reconstruction on real 2D MPI data with a trajectory-independent model-based MPI reconstruction algorithm. We further develop the zero-shot Plug-and-Play (PnP) algorithm of the authors -- with automatic noise level estimation -- to address the present deconvolution problem, leveraging a state-of-the-art denoiser trained on natural images without retraining on MPI-specific data. We evaluate our method on the publicly available 2D FFP MPI dataset ``MPIdata: Equilibrium Model with Anisotropy", featuring scans of six phantoms acquired using a Bruker preclinical scanner. Moreover, we show reconstruction performed on custom data on a 2D scanner with additional high-frequency excitation field and partial data. Our results demonstrate strong reconstruction capabilities across different scanning scenarios -- setting a precedent for general-purpose, flexible model-based MPI reconstruction.

cs.CV↗

arXiv2025

An $\ell^1$-Plug-and-Play Approach for MPI Using a Zero Shot Denoiser with Evaluation on the 3D Open MPI Dataset

Objective: Magnetic particle imaging (MPI) is an emerging medical imaging modality which has gained increasing interest in recent years. Among the benefits of MPI are its high temporal resolution, and that the technique does not expose the specimen to any kind of ionizing radiation. It is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. From the electric signal measured in receive coils, the particle concentration has to be reconstructed. Due to the ill-posedness of the reconstruction problem, various regularization methods have been proposed for reconstruction ranging from early stopping methods, via classical Tikhonov regularization and iterative methods to modern machine learning approaches. In this work, we contribute to the latter class: we propose a plug-and-play approach based on a generic zero-shot denoiser with an $\ell^1$-prior. Approach: We validate the reconstruction parameters of the method on a hybrid dataset and compare it with the baseline Tikhonov, DIP and the previous PP-MPI, which is a plug-and-play method with denoiser trained on MPI-friendly data. Main results: We offer a quantitative and qualitative evaluation of the zero-shot plug-and-play approach on the 3D Open MPI dataset. Moreover, we show the quality of the approach with different levels of preprocessing of the data. Significance: The proposed method employs a zero-shot denoiser which has not been trained for the MPI task and therefore saves the cost for training. Moreover, it offers a method that can be potentially applied in future MPI contexts.

eess.IV↗

arXiv2024

Variational Model-Based Reconstruction Techniques for Multi-Patch Data in Magnetic Particle Imaging

Magnetic Particle Imaging is an emerging imaging modality through which it is possible to detect tracers containing superparamagnetic nanoparticles. The exposure of the particles to dynamic magnetic fields generates a non-linear response that is used to locate the particles and produce an image of their distribution. The bounding box that can be covered by a single scan curve depends on the strength of the gradients of the magnetic fields applied, which is limited due to the risk of causing peripheral nerve stimulation (PNS) in the patients. To address this issue, multiple scans are performed. The scan data must be merged together to produce reconstructions of larger regions of interest. In this paper we propose a mathematical framework which can deal with rather general multi-patching scenarios including rigid transformations of the field of view (FoV), the specimen and of the scanner. We show the flexibility of this framework in a variety of different scanning scenarios. Moreover, we describe an iterative reconstruction algorithm that yields a reconstruction of the target distribution by minimizing a convex functional which includes positivity constraints and sparsity enforcing priors. We show its convergence to a minimizer and perform numerical experiments on simulated data.

math.NA↗