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REVIEW 3 major objections 4 minor 60 references

Learned Discrepancy Reconstruction and Benchmark Dataset for Magnetic Particle Imaging

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Replacing the Gaussian noise assumption with a learned flow-based discrepancy improves MPI reconstruction similarity at every tested tracer concentration.

desk verdict Real dataset, clean idea, but the central equation has a sign error that makes the printed method different from the one actually evaluated. read the letter →

arxiv 2501.05583 v1 pith:4I3WYZCE submitted 2025-01-09 math.NA cs.LGcs.NA

Meira Iske , Hannes Albers , Tobias Knopp , Tobias Kluth This is my paper · ORCID
classification math.NAcs.LGcs.NA MSC 65J2268T07
keywords magneticparticleimaginglearneddiscrepancyinvertibleneuralnetworknormalizingflowimagereconstructioninverseproblemsMPI-MNISTnoisemodeling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Magnetic particle imaging (MPI) reconstructs images from voltage measurements whose noise is not well described by the Gaussian model assumed in standard Tikhonov and Kaczmarz reconstructions. The paper introduces the Learned Discrepancy Approach (LDA), which replaces the usual squared-error discrepancy with one built from an invertible neural network trained on real scanner noise, and derives this objective from Bayesian maximum-a-posteriori estimation. It also introduces MPI-MNIST, a dataset of 70,000 simulated MPI measurements of handwritten digits with realistic measured scanner noise. Using that dataset, the paper reports that LDA attains the highest mean structural similarity at every tested tracer concentration, with the largest advantage at the lowest concentration (SSIM 0.9314 versus 0.8527 for regularized Kaczmarz at 2 mgFe/mL). This matters because the method provides a principled way to reconstruct when the noise model is unknown, and the new dataset gives other researchers the means to test it.

What carries the argument

The discrepancy network $\varphi_\theta$ is the load-bearing object: a multi-scale invertible neural network built from affine coupling layers, trained by maximum likelihood on approximately 300,000 measured noise samples. Through the change-of-variables formula, it turns the unknown noise distribution into a Gaussian latent distribution, so the negative log-likelihood of the residual $y^\delta - Ax$ becomes $\frac{1}{2}\|\varphi_\theta(y^\delta - Ax)\|^2 - \log|\det J_{\varphi_\theta}(y^\delta - Ax)|$. The log-determinant term is what distinguishes this from a mere learned whitening: it keeps the likelihood exact for non-Gaussian noise, and it is what carries the claimed reconstruction improvements.

What would settle it

Apply LDA to real MPI measurements of a physical phantom with known concentration, using the same system matrix calibration and noise sampling procedure: if its structural similarity advantage over regularized Kaczmarz does not reproduce there, the learned noise distribution does not transfer. A controlled version would add a slow scanner drift or non-additive perturbation to the test data and check whether the reported gains disappear.

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Extended reading notes

Core claim

Starting from the linear inverse problem $y^\delta = Ax + \eta$, the paper treats the noise density $p_H$ as unknown and represents it through a diffeomorphism $g$ using the change-of-variables identity $p_H(\eta) = p_Z(g(\eta))\,|\det J_g(\eta)|$, where $p_Z$ is a known latent density. An invertible neural network $\varphi_\theta$ is trained on empty-scanner noise samples to approximate $g$, and substituting the learned density into the maximum-a-posteriori objective yields the LDA minimizer $x_{\mathrm{LDA}} = \arg\min_x \frac{1}{2}\|\varphi_\theta(y^\delta - Ax)\|^2 - \log|\det J_{\varphi_\theta}(y^\delta - Ax)| - \log p_X(x)$. On the MPI-MNIST test set, the paper reports that this objective gives the highest mean structural similarity at all tested concentrations, with the largest gap at the highest noise level (SSIM 0.9314 for LDA versus 0.8527 for regularized Kaczmarz at 2 mgFe/mL). The method is presented as a post-processing refinement of a Kaczmarz reconstruction and as a general variational framework for linear inverse problems beyond MPI.

Load-bearing premise

The load-bearing premise is that the empty-scanner noise samples used to train the discrepancy network faithfully represent the additive noise present during real MPI measurements, and that this noise is independent of the phantom.

Editorial extensions

If this is right

  • MPI reconstruction no longer has to assume Gaussian noise; the discrepancy term can be fit to the scanner's measured noise.
  • Because LDA is formulated for general linear inverse problems, the same construction can be applied to other imaging modalities with structured noise.
  • MPI-MNIST gives the community 70,000 phantom-measurement pairs with several system-matrix models and noise levels, enabling reproducible algorithm comparison.
  • The reported gains are largest at low tracer concentration, where noise dominates, so LDA is most valuable in precisely the regime where classical methods struggle.
  • The cost is substantially more iterations and longer reconstruction times, which the paper identifies as a current limitation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the measured noise is actually non-additive or time-varying, the learned discrepancy would be misspecified; testing LDA on real phantom scans, rather than simulated data, is the direct next experiment.
  • The same learned-discrepancy idea could be paired with a learned prior, relaxing the Gaussian prior assumption in addition to the noise assumption.
  • The high iteration count makes LDA unsuitable for real-time imaging without acceleration, so a faster optimizer or a distilled approximation would be a natural engineering follow-up.
  • The dataset's multiple system matrices make it reusable for benchmarking operator-correction methods independently of noise-model learning.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes the Learned Discrepancy Approach (LDA) for linear inverse problems, in which the data discrepancy term of a Tikhonov-type objective is replaced by a learned log-likelihood of the noise, modeled by an invertible neural network trained on measured empty-scanner noise samples. It also introduces MPI-MNIST, a simulated benchmark of MNIST-derived phantoms with model-based MPI system matrices at several resolutions and additive noise frames from a preclinical Bruker scanner. In numerical experiments on this dataset, LDA initialized by regularized Kaczmarz reconstructions and minimized by gradient descent is reported to achieve the highest mean SSIM across all tested concentrations, with the largest gains at low concentration. The paper claims the method is applicable beyond MPI and that the dataset helps close the data gap in MPI.

Significance. The paper makes two useful contributions: a publicly accessible MPI benchmark with ground truth and realistic simulated measurements (Zenodo DOI), and a principled way of injecting a learned noise distribution into MAP estimation via a normalizing flow. The statistical derivation in Section 2.2 is clear, and the use of independent empty-scanner noise samples for training the discrepancy network avoids the most blatant form of circularity. The value is conditional, however: the experimental evidence is entirely simulated, with test noise drawn from the same scanner-noise population used for training, and hyperparameters are selected on test data. If the sign error in Eq. (2.10) is corrected and the evaluation is tightened, the method is a credible contribution to learned discrepancies for MPI and other inverse problems.

major comments (3)
  1. [Section 2.2, Eq. (2.10)] There is a sign inconsistency in the printed objective. Eq. (2.6) gives the MAP objective as argmin_x [ -log p(y_delta|x) - log p_X(x) ]. Substituting the flow-based noise density and using R(x) = -log p_X(x) as defined below Eq. (2.7) yields argmin_x [ D_theta(Ax,y_delta) + R(x) ], where D_theta(Ax,y_delta) = (1/2)||phi_theta(y_delta - Ax)||^2 - log|det J_phi_theta(y_delta - Ax)|. The printed Eq. (2.10), x_LDA = argmin_x D_theta(Ax,y_delta) - R(x), therefore has the wrong sign in front of R. For the implementation R(x) = (alpha/2)||x||^2 used in Section 6.1, the printed objective can be unbounded below when alpha is large or when the discretized forward operator is rank-deficient, so the stable and high-SSIM results in Table 1 cannot come from the objective as printed. The authors should correct the sign and state unambiguously which objective was used in the experiments: with the plus sign the method is the MAP estimator derived in the text; with the minus sign it is not, and the reported results would be unexplained.
  2. [Section 6.2 and Section 5.4.3] The empirical validation is in-distribution with respect to the noise. The discrepancy network is trained on roughly 300,000 noise samples from large_NoiseMeas.mdf, while the test measurements y_delta are generated by adding noise samples from the same scanner acquisition campaign (H^D_phantom) to simulated noiseless data. This demonstrates that LDA can exploit the specific noise population used during training, but it does not test performance under real forward measurements, operator error, drift, or non-additive disturbances. The authors should either temper the abstract and conclusion or add out-of-distribution experiments, for example noise from a different acquisition session, system-matrix mismatch with A_rec different from A_coarse_opt, or real MPI data. The current evidence supports a claim about the MPI-MNIST benchmark, not a claim about MPI scanner noise in general.
  3. [Section 6.1] The regularization parameters are selected on the test set: the grid search uses the first 100 images of the test dataset for Tikhonov, regularized Kaczmarz, and whitened regularized Kaczmarz, and the first 5 images for LDA, with SSIM as the selection criterion. The reported means over the full test set are therefore not independent generalization results, and the imbalance in tuning budget between LDA and the classical methods could bias the comparison. The authors should use a separate validation set for parameter selection, or explicitly present the current numbers as test-set-tuned performance rather than predictive performance on unseen data.
minor comments (4)
  1. [Section 4 and Section 5.4.2] The text contains two typos: 'noise sampes' in Section 4 should be 'noise samples', and 'seperate' in Section 5.4.2 should be 'separate'.
  2. [Figure 2 caption] The caption in Figure 2 reads 'PNSR' but should read 'PSNR'.
  3. [Section 6.1] Please specify the gradient descent step size and stopping criterion used for the LDA minimization. With 2000 iterations and RK initialization, the optimization protocol is part of the method and is not fully reproducible from the text.
  4. [Section 2.1, Eq. (2.3)] The sentence defining the entries w_j,j uses std(n_j), which should be std(eta_j) for consistency with the notation for the noise components introduced in the same equation.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the learned discrepancy is trained on independent scanner-noise samples and used in a standard MAP objective; the main caveats (self-created benchmark and an apparent sign error in Eq. (2.10)) are correctness and external-validity issues, not circularity.

full rationale

The derivation chain is self-contained rather than circular. The LDA objective follows from Bayes' theorem (Eqs. (2.4)-(2.6)), a change of variables (Eq. (2.8)), and a maximum-likelihood fit of the normalizing flow (Eq. (2.9)); the discrepancy network is trained on empty-scanner noise samples (Sections 4 and 6.2), not on the ground-truth phantoms or the reconstructed images, so the reported SSIM/PSNR gains are not forced by construction. The MPI-MNIST test set uses MNIST phantoms that were not used for training the flow, and the reconstruction target is the phantom, not the noise; the fact that test noise is drawn from the same scanner population as the training noise limits external validity but is not a circular reduction. No load-bearing self-citation or imported uniqueness theorem appears; citations to the authors' earlier MPI modeling work are background and domain support. Two non-circular caveats should be weighed separately. First, the evaluation is on a self-created simulated benchmark, and the paper itself states that validation on real MPI measurements is 'crucial for validating the method's generalizability' (Section 7). Second, Eq. (2.10) appears to have a sign error: with R(x) = -log pX(x) as defined below Eq. (2.7), the MAP derivation gives argmin D_theta(Ax, y^delta) + R(x), not D_theta - R(x); if implemented literally, the negative regularization term would reward large norms. This is a correctness and reproducibility defect in the method statement, not a circularity, and does not change the circularity score beyond 2.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the learned noise distribution from empty-scanner measurements, the additive noise assumption, the simulated Fokker-Planck system matrix, and the standard Bayesian MAP formalism. No new physical entities are invented. The main free parameters are the learned INN weights, per-method per-concentration regularization parameters, the system matrix mixing weights, and the hand-chosen frequency subset.

free parameters (4)
  • INN weights theta = approximately 13.9 million parameters
    Discrepancy network trained by maximum likelihood on about 300,000 empty-scanner noise samples in Section 6.2 and Appendix B; the learned discrepancy Dtheta is fully determined by these weights.
  • Regularization parameter alpha per method and concentration = not reported; selected by SSIM grid search
    Grid search over the first 100 test images for Tikhonov, RK, and WRK, and over the first 5 test images for LDA, at each concentration in Section 6.1. Values are not listed but enter every reported SSIM and PSNR number.
  • System matrix mixing weights W* = 5 by 12 matrix of nonnegative weights
    Estimated by least-squares fit of simulated Fokker-Planck matrices to measured Acalib in Eq. (3.2); Aopt used for all data generation depends on these weights.
  • Frequency index subset I = {50,...,813} = 50 to 813 of the 817 frequency components
    Band-pass selection by hand in Section 6; affects all compared methods equally and is a modeling choice rather than a fitted scalar.
assumptions (5)
  • domain assumption Measurement noise is additive and independent of the phantom, y_delta = y + eta with eta independent of x.
    The Bayesian factorization in Eq. (2.6) and p(y_delta|x) = pH(y_delta - Ax) require this; real scanner noise could include multiplicative or drift components.
  • domain assumption Empty-scanner noise samples are representative of the noise distribution during actual MPI imaging.
    Section 4 records noise with the scanner running empty for about one hour and Section 6.2 trains the discrepancy network on these samples; no real measured phantom validates transfer.
  • domain assumption The weighted Fokker-Planck system matrix Aopt approximates the measured scanner system matrix closely enough for simulated benchmarking.
    Eq. (3.2) estimates weights by least squares against Acalib, and all simulated measurements use Aopt; if this fit is poor, the benchmark may not represent a real MPI scanner.
  • standard math The change-of-variables formula and the chosen Gaussian latent density describe the true noise density.
    Eq. (2.8) is the standard density transformation for a diffeomorphism; the latent Gaussian is a modeling choice that limits the expressive class.
  • standard math The affine-coupling construction makes phi_theta invertible with tractable Jacobian determinant.
    Appendix B uses coupling, squeeze, split, and concatenation layers from RealNVP and Glow; this is standard, but the paper does not analyze approximation error of the flow.

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Cite this review

Pith. "Pith review of Learned Discrepancy Reconstruction and Benchmark Dataset for Magnetic Particle Imaging." pith.science (2026). https://pith.science/paper/4I3WYZCE

@misc{pith2026250105583,
  author       = {Pith},
  title        = {Pith review of: Learned Discrepancy Reconstruction and Benchmark Dataset for Magnetic Particle Imaging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4I3WYZCE}},
  note         = {Machine review of arXiv:2501.05583}
}
read the original abstract

Magnetic Particle Imaging (MPI) is an emerging imaging modality based on the magnetic response of superparamagnetic iron oxide nanoparticles to achieve high-resolution and real-time imaging without harmful radiation. One key challenge in the MPI image reconstruction task arises from its underlying noise model, which does not fulfill the implicit Gaussian assumptions that are made when applying traditional reconstruction approaches. To address this challenge, we introduce the Learned Discrepancy Approach, a novel learning-based reconstruction method for inverse problems that includes a learned discrepancy function. It enhances traditional techniques by incorporating an invertible neural network to explicitly model problem-specific noise distributions. This approach does not rely on implicit Gaussian noise assumptions, making it especially suited to handle the sophisticated noise model in MPI and also applicable to other inverse problems. To further advance MPI reconstruction techniques, we introduce the MPI-MNIST dataset - a large collection of simulated MPI measurements derived from the MNIST dataset of handwritten digits. The dataset includes noise-perturbed measurements generated from state-of-the-art model-based system matrices and measurements of a preclinical MPI scanner device. This provides a realistic and flexible environment for algorithm testing. Validated against the MPI-MNIST dataset, our method demonstrates significant improvements in reconstruction quality in terms of structural similarity when compared to classical reconstruction techniques.

Figures

Figures reproduced from arXiv: 2501.05583 by the authors.

Figure 1
Figure 1. Overview of the MPI-MNIST dataset and included reconstruction settings. [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. SSIM (left) and PNSR (right) values of the reconstruction methods evaluated over the test dataset [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Reconstructions of selected phantoms of the MPI-MNIST test dataset from different reconstruction [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

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Works this paper leans on

60 extracted references · 50 canonical work pages

  1. [1]

    Tomographic imaging using the nonlinear response of magnetic particles

    B Gleich and J Weizenecker. “Tomographic imaging using the nonlinear response of magnetic particles”. In: Nature 435 (2005), pp. 1214–7.doi: 10.1038/nature03808

    work page doi:10.1038/nature03808 2005

  2. [2]

    Magnetic particle imaging: From proof of principle to preclinical applications

    T Knopp, N Gdaniec, and M Möddel. “Magnetic particle imaging: From proof of principle to preclinical applications”.In: Physics in Medicine & Biology62.14(2017),R124. doi: 10.1088/1361-6560/aa6c99

    work page doi:10.1088/1361-6560/aa6c99 2017

  3. [3]

    Magnetic particle imaging: Introduction to imaging and hardware realization

    T Buzug, G Bringout, M Erbe, K Gräfe, M Graeser, M Grüttner, A Halkola, T Sattel, W Tenner, H Wojtczyk, J Haegele, F Vogt, J Barkhausen, and K Lüdtke-Buzug. “Magnetic particle imaging: Introduction to imaging and hardware realization”. In:Zeitschrift für Medizinische Physik22.4 (2012), pp. 323–334. doi: 10.1016/j.zemedi.2012.07.004

    work page doi:10.1016/j.zemedi.2012.07.004 2012

  4. [4]

    Experimental results on fast 2D-encoded magnetic particle imaging

    B Gleich, J Weizenecker, and J Borgert. “Experimental results on fast 2D-encoded magnetic particle imaging”. In:Physics in Medicine & Biology53.6 (2008), N81.doi: 10.1088/0031-9155/53/6/N01

    work page doi:10.1088/0031-9155/53/6/n01 2008

  5. [5]

    Online reconstruction of 3D magnetic particle imaging data

    T Knopp and M Hofmann. “Online reconstruction of 3D magnetic particle imaging data”. In:Physics in Medicine & Biology61.11 (2016), N257.doi: 10.1088/0031-9155/61/11/N257

    work page doi:10.1088/0031-9155/61/11/n257 2016

  6. [6]

    Magnetic particle imaging for quantification of vascular stenoses: A phantom study

    S Herz, P Vogel, T Kampf, M Rückert, S Veldhoen, V Behr, and T Bley. “Magnetic particle imaging for quantification of vascular stenoses: A phantom study”. In:IEEE Transactions on Medical Imaging 37.1 (2018), pp. 61–67.doi: 10.1109/TMI.2017.2717958

    work page arXiv 2018

  7. [7]

    Three-dimensional real-time in vivo magnetic particle imaging

    J Weizenecker, B Gleich, J Rahmer, H Dahnke, and J Borgert. “Three-dimensional real-time in vivo magnetic particle imaging”. In:Physics in Medicine & Biology54.5 (2009), p. L1.doi: 10.1088/0031- 9155/54/5/L01

    doi:10.1088/0031- 2009

  8. [8]

    Magnetic particle imaging for in vivo blood flow velocity measurements in mice

    Michael G Kaul, Johannes Salamon, Tobias Knopp, Harald Ittrich, Gerhard Adam, Horst Weller, and Caroline Jung. “Magnetic particle imaging for in vivo blood flow velocity measurements in mice”. In: Physics in Medicine & Biology63.6 (2018), p. 064001

    work page 2018

Show all 60 references
  1. [9]

    Magnetic particle imaging: Visualization of instruments for cardiovascular intervention

    J Haegele, J Rahmer, B Gleich, J Borgert, H Wojtczyk, N Panagiotopoulos, T Buzug, J Barkhausen, and F. Vogt. “Magnetic particle imaging: Visualization of instruments for cardiovascular intervention”. In: Radiology 265.3 (2012), pp. 933–938.doi: 10.1148/radiol.12120424

    2012 doi

  2. [10]

    Magnetic particle imaging–guided stenting

    S Herz, P Vogel, T Kampf, P Dietrich, S Veldhoen, M A. Rückert, R Kickuth, V Behr, and T Bley. “Magnetic particle imaging–guided stenting”. In:Journal of Endovascular Therapy26.4 (2019), pp. 512–519. doi: 10.1177/1526602819851202. 16

    2019 doi

  3. [11]

    Interactive magnetic catheter steering with 3-D real-time feedback using multi-color magnetic particle imaging

    J Rahmer, D Wirtz, C Bontus, J Borgert, and B Gleich. “Interactive magnetic catheter steering with 3-D real-time feedback using multi-color magnetic particle imaging”. In:IEEE Transactions on Medical Imaging 36.7 (2017), pp. 1449–1456.doi: 10.1109/TMI.2017.2679099

    2017

  4. [12]

    First dedicated balloon catheter for magnetic particle imaging

    M Ahlborg, T Friedrich, T Göttsche, V Scheitenberger, R Linemann, M Wattenberg, A T Buessen, T Knopp, P Szwargulski, M G Kaul, et al. “First dedicated balloon catheter for magnetic particle imaging”. In:IEEE transactions on medical imaging41.11 (2022), pp. 3301–3308

    2022

  5. [13]

    Quan- titative

    J Bulte, P Walczak, M Janowski, K Krishnan, H Arami, A Halkola, B Gleich, and J Rahmer. “Quan- titative "hot spot" imaging of transplanted stem cells using superparamagnetic tracers and magnetic particle imaging (MPI)”. In:Tomography1.2 (2015), pp. 91–97.doi: 10.18383/j.tom.2015.00172

    2015

  6. [14]

    A perspective on cell tracking with magnetic particle imaging

    O Sehl, J Gevaert, K Meli, N Knie, and P Foster. “A perspective on cell tracking with magnetic particle imaging”. In:Tomography6.4 (2020), pp. 315–324.doi: 10.18383/j.tom.2020.00043

    2020

  7. [15]

    In vivo cellular magnetic imaging: Labeled versus unlabeled cells

    Jeff WM Bulte, Chao Wang, and Ali Shakeri-Zadeh. “In vivo cellular magnetic imaging: Labeled versus unlabeled cells”. In:Advanced functional materials32.50 (2022), p. 2207626

    2022

  8. [16]

    Magnetic particle imaging: A novel in vivo imaging platform for cancer detection

    E Yu, M Bishop, B Zheng, R Ferguson, A Khandhar, S Kemp, K Krishnan, P Goodwill, and S Conolly. “Magnetic particle imaging: A novel in vivo imaging platform for cancer detection”. In:Nano Letters 17.3 (2017), pp. 1648–1654.doi: 10.1021/acs.nanolett.6b04865

    2017 doi

  9. [17]

    High-performance iron oxide nanoparticles for magnetic particle imaging–guided hyperthermia (hMPI)

    L M Bauer, S F Situ, M A Griswold, and A C S Samia. “High-performance iron oxide nanoparticles for magnetic particle imaging–guided hyperthermia (hMPI)”. In:Nanoscale 8.24 (2016), pp. 12162–12169

    2016

  10. [18]

    Weighted iterative reconstruction for magnetic particle imaging

    T Knopp, J Rahmer, T Sattel, S Biederer, J Weizenecker, B Gleich, J Borgert, and T Buzug. “Weighted iterative reconstruction for magnetic particle imaging”. In:Physics in Medicine & Biology55.6 (2010), p. 1577. doi: 10.1088/0031-9155/55/6/003

    2010 doi

  11. [19]

    Singular value analysis for magnetic particle imaging

    T Knopp, S Biederer, T Sattel, and T Buzug. “Singular value analysis for magnetic particle imaging”. In: 2008 IEEE Nuclear Science Symposium Conference Record. 2008, pp. 4525–4529.doi: 10.1109/ NSSMIC.2008.4774296

    2008

  12. [20]

    Model- based reconstruction for magnetic particle imaging

    T Knopp, T Sattel, S Biederer, J Rahmer, J Weizenecker, B Gleich, J Borgert, and T Buzug. “Model- based reconstruction for magnetic particle imaging”. In:IEEE Transactions on Medical Imaging29.1 (2010), pp. 12–18.doi: 10.1109/TMI.2009.2021612

    2010

  13. [21]

    2D model-based reconstruction for magnetic particle imaging

    T Knopp, S Biederer, T Sattel, J Rahmer, J Weizenecker, B Gleich, J Borgert, and T Buzug. “2D model-based reconstruction for magnetic particle imaging”. In:Medical Physics37.2 (2010), pp. 485–

    2010

  14. [22]

    Nonlinear behavior of magnetic fluid in Brownian relaxation: Numerical simulation and derivation of empirical model

    T Yoshida and K Enpuku. “Nonlinear behavior of magnetic fluid in Brownian relaxation: Numerical simulation and derivation of empirical model”. In:Magnetic Particle Imaging. Ed. by Thorsten M. Buzug and Jörn Borgert. Springer Berlin Heidelberg, 2012

    2012

  15. [23]

    Mathematical models for magnetic particle imaging

    T Kluth. “Mathematical models for magnetic particle imaging”. In: Inverse Problems 34.8 (2018), p. 083001. doi: 10.1088/1361-6420/aac535

    2018 doi

  16. [24]

    Towards accurate modeling of the multidimensional magnetic particle imaging physics

    T Kluth, P Szwargulski, and T Knopp. “Towards accurate modeling of the multidimensional magnetic particle imaging physics”. In:New Journal of Physics21.10 (2019), p. 103032.doi: 10.1088/1367- 2630/ab4938

    2019 doi

  17. [25]

    Modeling the magnetization dynamics for largeensemblesofimmobilizedmagneticnanoparticlesinmulti-dimensionalmagneticparticleimaging

    H Albers, T Knopp, M Möddel, M Boberg, and T Kluth. “Modeling the magnetization dynamics for largeensemblesofimmobilizedmagneticnanoparticlesinmulti-dimensionalmagneticparticleimaging”. In: Journal of Magnetism and Magnetic Materials543 (2022), p. 168534.doi: 10.1016/j.jmmm.20...

    2022 doi

  18. [26]

    Equilibrium model with anisotropy for model-based reconstruction in magnetic particle imaging

    M Maass, T Kluth, C Droigk, H Albers, K Scheffler, A Mertins, and T Knopp. “Equilibrium model with anisotropy for model-based reconstruction in magnetic particle imaging”. In:IEEE Transactions on Computational Imaging10 (2024), pp. 1588–1601.doi: 10.1109/TCI.2024.3490381

    2024

  19. [27]

    Sensitivity enhance- ment in magnetic particle imaging by background subtraction

    K Them, M Kaul, C Jung, M Hofmann, T Mummert, F Werner, and T Knopp. “Sensitivity enhance- ment in magnetic particle imaging by background subtraction”. In:IEEE Transactions on Medical Imaging 35.3 (2015), pp. 893–900.doi: 10.1109/TMI.2015.2501462

    2015

  20. [28]

    Correction of linear system drifts in magnetic particle imaging

    T Knopp, N Gdaniec, R Rehr, M Graeser, and T Gerkmann. “Correction of linear system drifts in magnetic particle imaging”. In:Physics in Medicine & Biology64.12 (2019), p. 125013.doi: 10.1088/ 1361-6560/ab2480

    2019

  21. [29]

    Enhanced reconstruction in magnetic particle imaging by whitening and random- ized SVD approximation

    T Kluth and B Jin. “Enhanced reconstruction in magnetic particle imaging by whitening and random- ized SVD approximation”. In:Physics in Medicine & Biology64.12 (2019), p. 125026.doi: 10.1088/ 1361-6560/ab1a4f. 17

    2019

  22. [30]

    Model uncertainty in magnetic particle imaging: Nonlinear problem formulation and model-based sparse reconstruction

    T Kluth and P Maass. “Model uncertainty in magnetic particle imaging: Nonlinear problem formulation and model-based sparse reconstruction”. In:International Journal of Magnetic Particle Imaging3.2 (2017). doi: 10.18416/ijmpi.2017.1707004

    2017

  23. [31]

    Inverse problems with inexact forward operator: Iterative regu- larization and application in dynamic imaging

    S Blanke, B Hahn, and A Wald. “Inverse problems with inexact forward operator: Iterative regu- larization and application in dynamic imaging”. In:Inverse Problems 36.12 (2020), p. 124001. doi: 10.1088/1361-6420/abb5e1

    2020 doi

  24. [33]

    Improved image reconstruction in magnetic particle imaging using structural a priori information

    C Bathke, T Kluth, C Brandt, and P Maass. “Improved image reconstruction in magnetic particle imaging using structural a priori information”. In:International Journal of Magnetic Particle Imaging 3.1 (2017). doi: 10.18416/ijmpi.2017.1703015

    2017

  25. [34]

    Edge preserving and noise reducing reconstruction for magnetic particle imaging

    M Storath, C Brandt, M Hofmann, T Knopp, J Salamon, A Weber, and A Weinmann. “Edge preserving and noise reducing reconstruction for magnetic particle imaging”. In:IEEE Trans Med Imaging36.1 (2017). doi: 10.1109/TMI.2016.2593954

    2017

  26. [35]

    L1 data fitting for robust reconstruction in magnetic particle imaging: Quantitative evalu- ation on Open MPI dataset

    T Kluth. “L1 data fitting for robust reconstruction in magnetic particle imaging: Quantitative evalu- ation on Open MPI dataset”. In:International Journal on Magnetic particle Imaging6.2 (2020). doi: 10.18416/IJMPI.2020.2012001

    2020

  27. [36]

    A deep learning approach for automatic image reconstruction in MPI

    T Knopp, P Jürß, and M Grosser. “A deep learning approach for automatic image reconstruction in MPI”. In:International Journal of Magnetic Particle Imaging9.1 (2023).doi: 10.18416/ijmpi.2023. 2303008

    2023 doi

  28. [37]

    Data augmentation for training a neural network for image reconstruction in MPI

    A von Gladiss, I Kramer, N Theisen, R Memmesheimer, A Bakenecker, T Buzug, and D Paulus. “Data augmentation for training a neural network for image reconstruction in MPI”. In:International Journal of Magnetic Particle Imaging8.1 (2022). doi: 10.18416/ijmpi.2022.2203058

    2022

  29. [38]

    Reconstruction of 1D images with a neural network for magnetic particle imaging

    A von Gladiss, R Memmesheimer, N Theisen, A Bakenecker, T Buzug, and D Paulus. “Reconstruction of 1D images with a neural network for magnetic particle imaging”. In:Bildverarbeitung für die Medizin

  30. [39]

    Neural network for reconstruction of MPI images

    P Koch, M Maass, M Bruhns, C Droigk, T Parbs, and A Mertins. “Neural network for reconstruction of MPI images”. In:9th International Workshop on Magnetic Particle Imaging (IWMPI). 2019

    2019

  31. [40]

    PP-MPI: A deep plug- and-play prior for magnetic particle imaging reconstruction

    B Askin, A Güngör, D Alptekin Soydan, E Saritas, C Top, and T Cukur. “PP-MPI: A deep plug- and-play prior for magnetic particle imaging reconstruction”. In:Machine Learning for Medical Image Reconstruction. Springer International Publishing, 2022, pp. 105–114

    2022

  32. [41]

    A denoiser scaling technique for plug-and-play MPI reconstruction

    A Güngör, B Askin, D Soydan, E Saritas, C Top, and T Çukur. “A denoiser scaling technique for plug-and-play MPI reconstruction”. In:International Journal of Magnetic Particle Imaging. Vol. 9

  33. [43]

    DEQ-MPI: A deep equilibrium reconstruction with learned consistency for magnetic particle imaging

    A Güngör, B Askin, D A Soydan, C B Top, E U Saritas, and T Çukur. “DEQ-MPI: A deep equilibrium reconstruction with learned consistency for magnetic particle imaging”. In: IEEE Transactions on Medical Imaging43.1 (2023), pp. 321–334

    2023

  34. [44]

    A deep equilibrium technique for 3D MPI reconstruction

    A Güngör, E Saritas, and T Çukur. “A deep equilibrium technique for 3D MPI reconstruction”. In: International Journal of Magnetic Particle Imaging. Vol. 10. 1. 2024.doi: 10.18416/ijmpi.2024. 2403009

    2024 doi

  35. [45]

    Deep image prior for 3D magnetic particle imaging: A quantitative comparison of regularization techniques on Open MPI dataset

    S Dittmer, T Kluth, M Henriksen, and P Maass. “Deep image prior for 3D magnetic particle imaging: A quantitative comparison of regularization techniques on Open MPI dataset”. In:International Journal on Magnetic Particle Imaging7.1 (2021). doi: 10.18416/IJMPI.2021.2103001

    2021

  36. [46]

    OpenMPIData: An initiative for freely accessible magnetic particle imaging data

    T Knopp, P Szwargulski, F Griese, and M Gräser. “OpenMPIData: An initiative for freely accessible magnetic particle imaging data”. In:Data in Brief 28 (2020), p. 104971.doi: 10.1016/j.dib.2019. 104971. 18

    2020 doi

  37. [47]

    Deep learning for improving the spatial resolution of magnetic particle imaging

    Y Shang, J Liu, L Zhang, X Wu, P Zhang, L Yin, H Hui, and J Tian. “Deep learning for improving the spatial resolution of magnetic particle imaging”. In:Physics in Medicine & Biology67.12 (2022), p. 125012. doi: 10.1088/1361-6560/ac6e24

    2022 doi

  38. [48]

    Shared prior learning of energy-based models for image reconstruction

    T Pinetz, E Kobler, T Pock, and A Effland. “Shared prior learning of energy-based models for image reconstruction”. In: SIAM Journal on Imaging Sciences14.4 (2021), pp. 1706–1748. doi: 10.1137/ 20M1380016

    2021

  39. [49]

    8. Bilevel approaches for learning of variational imaging models

    L Calatroni, C Cao, J C De los Reyes, C-B Schönlieb, and T Valkonen. “8. Bilevel approaches for learning of variational imaging models”. In:Variational Methods: In Imaging and Geometric Control. Ed. by M Bergounioux, G Peyré, C Schnörr, J-B Caillau, and T Haberkorn. Berlin, Bo...

    2017 doi

  40. [50]

    The MNIST database of handwritten digits

    Y LeCun. The MNIST database of handwritten digits. 1998. url: http://yann.lecun.com/exdb/ mnist/

    1998

  41. [51]

    On row relaxation methods for large constrained least squares problems

    A Dax. “On row relaxation methods for large constrained least squares problems”. In:SIAM Journal on Scientific Computing14.3 (1993), pp. 570–584.doi: 10.1137/0914036

    1993 doi

  42. [52]

    H Albers, T Kluth, and T Knopp. “Simulating magnetization dynamics of large ensembles of single domain nanoparticles: Numerical study ofBrown/Néel dynamicsand parameter identification problems in magnetic particle imaging”. In:Journal of Magnetism and Magnetic Materials541 (20...

    2022

  43. [53]

    Experimental parameter calibration of the scanner model for model-based MPI

    F Thieben, H Albers, F Mohn, F Foerger, M Boberg, K Scheffler, M Möddel, T Kluth, and T Knopp. “Experimental parameter calibration of the scanner model for model-based MPI”. In:International Journal on Magnetic Particle Imaging IJMPI(2024). doi: 10.18416/IJMPI.2024.2403025

    2024

  44. [54]

    Statistical and Computational Inverse Problems

    J Kaipio and E Somersalo. Statistical and Computational Inverse Problems. Springer New York, NY, 2004

    2004

  45. [55]

    T Knopp, T Viereck, G Bringout, M Ahlborg, J Rahmer, and M Hofmann.MDF: Magnetic particle imaging data format. 2020. doi: 10.48550/arxiv.1602.06072. url: https://arxiv.org/abs/1602. 06072

    2020 doi arXiv

  46. [56]

    Solving the MPI reconstruction problem with automatically tuned regularization parameters

    K Scheffler, M Boberg, and T Knopp. “Solving the MPI reconstruction problem with automatically tuned regularization parameters”. In: Physics in Medicine & Biology 69.4 (2024), p. 045024. doi: 10.1088/1361-6560/ad2231

    2024 doi

  47. [57]

    Image quality assessment: From error visibility to structural similarity

    Z Wang, A Bovik, H Sheikh, and E Simoncelli. “Image quality assessment: From error visibility to structural similarity”. In: IEEE Transactions on Image Processing 13.4 (2004), pp. 600–612. doi: 10.1109/TIP.2003.819861

    2004

  48. [58]

    Glow: Generative flow with invertible 1x1 convolutions

    D Kingma and P Dhariwal. “Glow: Generative flow with invertible 1x1 convolutions”. In:Advances in neural information processing systems. Ed. by S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett. Vol. 31. Curran Associates, Inc., 2018

    2018

  49. [59]

    Density estimation using Real NVP

    L Dinh, J Sohl-Dickstein, and S Bengio. “Density estimation using Real NVP”. In:ICLR. 2017. A Modifications of MPI-MNIST The fully provided dataset described in Section 5 contains preselected parameters such as a fixed particle concentration, reconstruction resolution, as well...

    2017

  50. [491]

    doi: 10.1118/1.3271258

    doi

  51. [2022]

    by Klaus Maier-Hein, Thomas M

    Ed. by Klaus Maier-Hein, Thomas M. Deserno, Heinz Handels, Andreas Maier, Christoph Palm, and Thomas Tolxdorff. Springer Fachmedien Wiesbaden, 2022, pp. 247–252.doi: 10.1007/978- 3- 658-36932-3_52

    2022 doi

  52. [2023]

    doi: 10.18416/ijmpi.2023.2303041

    2023

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.