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arxiv: 2601.07531 · v2 · submitted 2026-01-12 · ⚛️ physics.med-ph

Recognition: 2 theorem links

· Lean Theorem

Standardized Images and Evaluation Metrics for Tomography

Anna Frixou , Theodoros Leontiou , Efstathios Stiliaris , Costas N. Papanicolas
Authors on Pith no claims yet

Pith reviewed 2026-05-16 15:15 UTC · model grok-4.3

classification ⚛️ physics.med-ph
keywords tomographyreconstruction evaluationreference imagesSPECTimage metricsMLEMdiagnostic toolsquantitative assessment
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The pith

Four standardized reference images and sensitive metrics expose discrepancies in tomographic reconstructions that global scores like SSIM and PSNR miss.

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

The paper proposes a framework for evaluating tomographic reconstructions built around four reference images derived from physical modeling, each marking a distinct stage from source emission through detector response to ideal and realistic outputs. These are paired with diagnostic tools such as pixel-wise chi-squared maps, difference maps, spectral decomposition of intensities, and region-of-interest metrics that remain informative in high-fidelity regimes where conventional global measures saturate. A sympathetic reader would care because modern reconstruction algorithms produce outputs so close that broad similarity scores cannot separate meaningful physical differences from residual artifacts. Tests on MLEM and RISE-1 methods with software phantoms illustrate that the new tools detect discrepancies overlooked by standard metrics. The approach is framed as generalizable to other tomographic modalities for reproducible, stage-specific assessment.

Core claim

The authors establish a standardized quantitative framework consisting of four reference images—Source, Detector, Ideal, and Realistic—each obtained from physical modeling to represent successive stages in the imaging and reconstruction chain, together with a suite of diagnostic and quantitative tools including pixel-wise χ² and difference maps, spectral decomposition of intensity distributions, and RoI-based metrics. Application to MLEM and RISE-1 reconstructions on software phantoms shows these components expose discrepancies that conventional global metrics such as SSIM, PSNR, NMSE, and CC fail to detect, while the methodology is presented as applicable beyond SPECT.

What carries the argument

The four standardized reference images (Source, Detector, Ideal, Realistic) derived from physical modeling, together with the suite of sensitive tools (pixel-wise χ² maps, difference maps, spectral decomposition, RoI metrics) that operate where global metrics saturate.

If this is right

  • Reconstructions become comparable at specific physical stages rather than solely through overall image similarity scores.
  • Discrepancies between advanced methods such as MLEM and RISE-1 become quantifiable even when images appear nearly identical under global metrics.
  • Evaluation gains reproducibility and physical interpretability for high-performance regimes across tomographic modalities.
  • Algorithm development can target errors identified at particular stages in the source-to-output chain.
  • Conventional metrics that lose resolution in high-fidelity cases are supplemented by localized and spectral diagnostics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same staged reference set could be applied to real detector data to test whether software-phantom results hold under experimental noise.
  • Spectral decomposition might be extended to isolate frequency bands associated with common reconstruction artifacts in specific algorithms.
  • Integration with parameter optimization loops could use stage-specific metric feedback to adjust reconstruction settings automatically.
  • Fields such as CT or PET could adopt parallel reference-image suites to create cross-modality benchmarks for high-fidelity performance.

Load-bearing premise

The four reference images accurately represent distinct stages in the imaging and reconstruction chain, and the new metrics remain sensitive without introducing their own biases or saturation effects.

What would settle it

If the pixel-wise χ² maps, spectral components, or RoI metrics return statistically indistinguishable values for MLEM and RISE-1 reconstructions on the same software phantoms while independent physical analysis confirms real differences in fidelity, the claim of superior sensitivity would be challenged.

Figures

Figures reproduced from arXiv: 2601.07531 by Anna Frixou, Costas N. Papanicolas, Efstathios Stiliaris, Theodoros Leontiou.

Figure 1
Figure 1. Figure 1: Graphical representation of the specific activity of the two-dimensional “Source Images” of the Shepp–Logan phantom. Selected Regions of Interest (RoIs) are shown and will be discussed at Section 2.4.3. In the modified Shepp–Logan phantom version used in this work, the cranial bone has been removed, while the major large ellipsoid representing the brain grey and white serves also as a background source. Ge… view at source ↗
Figure 2
Figure 2. Figure 2: “Source” and “Detector” images from simulations of the modified SheppLogan phantom. The “Source Image” includes all emitted photons; the “Detector” image includes only detected ones. The rightmost panels show their difference; photon absorption and scattering within the phantom is the dominant effect. In practical imaging scenarios, no matter how advanced the reconstruction method￾ology is, the resulting i… view at source ↗
Figure 3
Figure 3. Figure 3: Simulated Shepp–Logan image of the Source Image and the Ideal Image, together with their difference. https://doi.org/10.3390/tomography12040049 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Difference and χ 2 map of images and sinograms. In the first row, the sinogram corre￾sponding to an Ideal Image of a Shepp–Logan phantom and the sinogram resulting from an MLEM reconstruction are shown along with the resulting sinogram difference and χ 2 map. In the second row, the Ideal Image from a Shepp–Logan phantom, the MLEM reconstructed image, their differ￾ence, and the corresponding χ 2 map are sho… view at source ↗
Figure 5
Figure 5. Figure 5: The intensity histograms (on logarithmic and linear scale) of “Ideal” and reconstructed images (on the left) and sinograms (on the right) of [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The top row depicts the “Ideal Sinogram” (a) and those resulting from different stages of MLEM (3, 9, 24, and 48 iterations) (be). The bottom row shows the “Ideal Image” (f) and the corresponding MLEM reconstructions (gj). https://doi.org/10.3390/tomography12040049 [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: A selection of metrics (NMSE, PSNR, CC, SSIM, CNR, and SCI) are presented for each one of the RoIs and the entire image, and for four stages of MLEM evolution. The SCI computed from the difference map between reconstructed and reference images. SSIM approaches unity at early reconstruction stages, whereas the SCI continues to evolve, indicating sensitivity to residual structure beyond global similarity. 3.… view at source ↗
Figure 8
Figure 8. Figure 8: The first row provides the difference and χ 2 maps for the sinogram and the second one the difference and χ 2 maps for the images. The difference and χ 2 maps reveal areas of the images that are not well-represented by the reconstruction. 3.1.2. Structure and Contrast Index (SCI) of Images and Sinograms The Structure and Contrast Index (SCI) is the metric we introduced to quantify the magnitude of the disc… view at source ↗
Figure 9
Figure 9. Figure 9: Convergence of the SCI. The structure, contrast, and SCI are computed from the difference map between reconstructed (four MLEM stages) and reference images in (a) and sinograms in (b). 3.1.3. Intensity (Gray-Value) Histogram Analysis of Images and Sinograms We have introduced the intensity (gray-value) histogram analysis of tomographic im￾ages and their corresponding sinograms as an additional diagnostic t… view at source ↗
Figure 10
Figure 10. Figure 10: The top row of the figure displays the “Ideal Image” alongside the four MLEM reconstruc￾tions. In the second row, the intensity histograms of the “Ideal Image” and each of the four recon￾structions are illustrated on the left. On the right, the intensity histograms of the “Ideal Sinogram” and those resulting from MLEM are presented. Linear and logarithmic scales are shown to visual￾ize both dominant and l… view at source ↗
Figure 11
Figure 11. Figure 11: The top row of the figure displays the “Ideal Image” alongside the three reconstructions from MLEM at full convergence and with 32, 64, and 256 projections. In the second row, the in￾tensity histograms of the “Ideal Image” and each of the three reconstructions are illustrated on the left. On the right, the intensity histograms of the “Ideal Sinogram” and those resulting from 32, 64, and 256 projections ar… view at source ↗
Figure 12
Figure 12. Figure 12: The top row of the figure displays the “Ideal Image” alongside the four reconstructions from MLEM at full convergence, utilizing sinograms with different level of statistics (1/8, 1/4, 1/2, and full counts). In the second row, the intensity histograms of the “Ideal Image” and each of the four reconstructions are illustrated on the left. On the right, the intensity histograms of the “Ideal Sinograms” with … view at source ↗
Figure 13
Figure 13. Figure 13: Top row: (a) “Ideal Sinogram” and sinograms obtained using three reconstruction meth￾ods: (b) ART, (c) MLEM, and (d) RISE-1. Bottom row: (e) Ideal Image and corresponding reconstruc￾tions: (f) ART, (g) MLEM, and (h) RISE-1. The examination of the metrics associated with the overall reconstruction ( [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The top-left and bottom-left panels show the difference maps (reconstruction—“Ideal”) and χ 2 maps for images and sinograms, for the three reconstruction methods (ART, MLEM, and RISE-1). The right panels present the corresponding residual intensities and χ 2 histograms. The χ 2 reduced values for both images and sinograms are reported in the bottom χ 2 histograms for each reconstruction method. https://do… view at source ↗
Figure 15
Figure 15. Figure 15: The panels show three RoIs from the phantom. The top row presents the “Ideal Image”, followed by reconstructions obtained with ART, MLEM, and RISE-1 in the subsequent rows. The images are normalized with reference to “Ideal Image”. The image intensity histograms and sinogram intensity histograms ( [PITH_FULL_IMAGE:figures/full_fig_p030_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The metrics NMSE, PSNR, CC, CNR, SSIM, and SCI are presented for each one of the RoIs and the entire image, across the three reconstruction techniques: ART, MLEM, and RISE-1. The SCI computed from the difference map between reconstructed and reference area. The reconstructions shown correspond to the high-background phantom configuration described in Section 3.2 and Ta￾ble 1, which is substantially more c… view at source ↗
Figure 17
Figure 17. Figure 17: Left: Intensity histograms of the “Ideal Image” (blue bars) and reconstructions obtained using ART (red line), MLEM (black line), and RISE-1 (blue line). Right: Intensity histograms of the “Ideal Sinogram” (blue bars) and corresponding ones from ART (red line), MLEM (black line), and RISE-1 (blue line). Both linear and logarithmic scales are shown to highlight dominant as well as low￾frequency components … view at source ↗
Figure 18
Figure 18. Figure 18: Left: “Detector” sinogram. Top row: Reconstructed image and sinogram without attenuation correction (NC). Bottom row: Reconstructed image and sinogram with attenuation correction (AC). Quantitative evaluation was performed by comparing the reconstructed sinograms to the “Detector” sinograms, and the results are summarized in [PITH_FULL_IMAGE:figures/full_fig_p033_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Top row: χ 2 maps comparing the reconstructed sinograms to the “Detector” sinograms for both cases NC and AC. Bottom row: Difference maps comparing the reconstructed sinograms to the “Detector” sinograms for both cases NC and AC. They clearly indicate that the AC sinogram represents the “Detector” sinogram more accurately, especially in the central region. The NC case exhibits a considerable discrep￾ancy … view at source ↗
Figure 20
Figure 20. Figure 20: Sinogram intensity histogram of the detector data and the reconstructed sinograms with and without attenuation correction. Panel (a) shows the intensity histograms on a logarithmic scale and panel (b) on a linear scale. Linear and logarithmic scales are shown to visualize both dominant and low-frequency components of the gray-value distribution. Even in clinical settings, where ground truth is not directl… view at source ↗
Figure 21
Figure 21. Figure 21: Reconstructed DATSCAN SPECT images of a Parkinsonian patient without attenuation correction (NC) (left) and with attenuation correction (AC) (right). The red rectangle indicates the Region of Interest (RoI) used for calculating the Contrast-to-Noise Ratio (CNR) directly from the re￾constructed images. Since no ground-truth phantom exists for clinical data, the CNR was estimated using the mean activity ins… view at source ↗
read the original abstract

Advances in instrumentation and computation have enabled increasingly sophisticated tomographic reconstruction methods. However, existing evaluation practices -- often based on simple phantoms and global image metrics -- are limited in their ability to differentiate among modern high-fidelity reconstructions. A standardized, quantitative framework capable of revealing subtle yet meaningful differences is therefore required. We introduce such a framework, built upon two core components. The first is a set of four standardized reference images -- Source, Detector, Ideal, and Realistic -- each derived from physical modeling and representing a distinct stage in the imaging and reconstruction chain. The second is a suite of diagnostic and quantitative tools that remain sensitive in regimes where conventional metrics (e.g., SSIM, PSNR, NMSE, CC) tend to saturate. These include pixel-wise $\chi^2$ and difference maps, their quantitative characterization, spectral decomposition of intensity distributions, and Region-of-Interest (RoI)-based metrics. Application of this framework to MLEM and RISE-1 reconstructions using software phantoms demonstrates its ability to expose discrepancies that might elude detection by conventional global metrics. While developed in the context of SPECT, the methodology generalizes to other tomographic modalities, providing a reproducible, interpretable, and physically grounded basis for evaluating reconstruction fidelity in the high-performance regime.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper proposes a standardized quantitative framework for evaluating tomographic reconstructions (focused on SPECT), consisting of four physically modeled reference images (Source, Detector, Ideal, Realistic) that represent distinct stages in the imaging chain, together with diagnostic tools including pixel-wise χ² and difference maps, spectral decomposition of intensity distributions, and Region-of-Interest metrics. These are claimed to remain sensitive in high-fidelity regimes where conventional global metrics (SSIM, PSNR, NMSE, CC) saturate. The framework is demonstrated on MLEM and RISE-1 reconstructions of software phantoms, where it is said to expose discrepancies not detected by standard metrics, and the approach is asserted to generalize to other modalities.

Significance. If the central claim holds, the framework would offer a reproducible, physically grounded alternative for distinguishing subtle differences among advanced reconstruction algorithms, addressing a recognized limitation of global metrics in the high-performance regime. The emphasis on standardized references derived from physical modeling and the provision of multiple diagnostic layers (maps plus spectral/RoI analysis) are constructive contributions that could improve interpretability and reproducibility in medical imaging evaluation.

major comments (2)
  1. [Abstract and application section] The validation is performed exclusively on software phantoms (Abstract and application section). Because these phantoms employ idealized forward models and noise statistics that match the reference-image generation assumptions exactly, the reported ability of the new metrics to expose discrepancies may be inflated; the manuscript must either add results on real SPECT acquisitions (with unmodeled scatter, attenuation errors, and detector non-uniformities) or provide a quantitative sensitivity analysis showing that the advantage persists under realistic perturbations.
  2. [Abstract and Results] No quantitative error analysis, statistical significance tests, or saturation thresholds for the conventional metrics are supplied to support the claim that the new suite 'exposes discrepancies that might elude detection' (Abstract). The manuscript should include tabulated comparisons (e.g., metric values and their dynamic ranges) and error bars across multiple realizations to make the superiority claim load-bearing rather than qualitative.
minor comments (3)
  1. [Methods] The precise definitions and generation procedures for the four reference images (Source, Detector, Ideal, Realistic) are not given as equations or pseudocode; reproducibility would be improved by explicit formulas in the Methods section.
  2. [Methods] The term 'spectral decomposition of intensity distributions' is introduced without specifying the transform (Fourier, wavelet, etc.) or the quantitative features extracted; clarify the implementation and any chosen frequency bands.
  3. [Abstract] The abstract states that the methodology 'generalizes to other tomographic modalities' but provides no concrete example or adaptation steps; a brief discussion or reference to a second modality would strengthen the claim.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the insightful comments, which have helped strengthen the manuscript. We address each major point below, incorporating revisions where feasible while maintaining the focus on the proposed framework.

read point-by-point responses

  1. Referee: Validation performed exclusively on software phantoms with idealized forward models matching reference assumptions exactly; must add real SPECT acquisitions or quantitative sensitivity analysis under realistic perturbations.

    Authors: We agree that matching assumptions in software phantoms can limit generalizability. In the revised manuscript we have added a dedicated sensitivity analysis section, applying controlled perturbations (e.g., 5–15% errors in attenuation maps and scatter estimates) to the forward model across 20 realizations and showing that the new metrics retain superior dynamic range and discrimination power compared with SSIM/PSNR/NMSE. Real clinical SPECT data would require separate experimental validation outside the current scope; we have noted this limitation and outlined plans for future work. revision: partial

  2. Referee: No quantitative error analysis, statistical significance tests, or saturation thresholds supplied; need tabulated comparisons, dynamic ranges, and error bars across realizations.

    Authors: We have expanded the Results section with new tables that report mean metric values and standard deviations over 10 independent noise realizations for both MLEM and RISE-1. Saturation thresholds are now defined quantitatively (e.g., SSIM > 0.98 where further differentiation fails) and supported by paired t-test p-values demonstrating statistically significant differences captured by the proposed χ² and spectral metrics but missed by global measures. revision: yes

standing simulated objections not resolved
  • Addition of results on real SPECT acquisitions with unmodeled physical effects, as this requires new experimental datasets not available in the present software-phantom study.

Circularity Check

0 steps flagged

No significant circularity; metrics and references defined from physical modeling and standard statistics

full rationale

The four reference images (Source, Detector, Ideal, Realistic) are constructed from explicit physical modeling stages rather than fitted to the target reconstructions. The diagnostic tools (pixel-wise χ² maps, difference maps, spectral decomposition of intensity distributions, RoI metrics) are standard statistical operations applied to those references. No equations reduce the claimed sensitivity advantage to a self-referential definition, fitted parameter, or self-citation chain. The demonstration on software phantoms is presented as an application, not as a derivation that forces the result by construction. The framework remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on domain assumptions about physical modeling of the imaging chain; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Physical models used to generate the Source, Detector, Ideal, and Realistic reference images accurately capture the distinct stages of the tomography process.
    Invoked to justify the reference images as standardized benchmarks.

pith-pipeline@v0.9.0 · 5537 in / 1090 out tokens · 109565 ms · 2026-05-16T15:15:57.275796+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We introduce such a framework, built upon two core components. The first is a set of four standardized reference images — Source, Detector, Ideal, and Realistic — each derived from physical modeling... The second is a suite of diagnostic and quantitative tools... pixel-wise χ² and difference maps... Structure and Contrast Index (SCI)

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The SCI is defined as the product of the contrast and structure components... evaluated on the difference map R... quantifies the extent to which the residual map contains coherent, spatially organized structure

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uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 1 internal anchor

  1. [1]

    On Hallucinations in Tomographic Image Reconstruction

    Bhadra, S.; Kelkar, V .A.; Brooks, F.J.; Anastasio, M.A. On Hallucinations in Tomographic Image Reconstruction. IEEE T rans. Med Imaging 2021, 40, 3249–3260. https://doi.org/10.1109/TMI.2021.3077857

    work page doi:10.1109/tmi.2021.3077857 2021

  2. [2]

    Deep learning for unsupervised domain adaptation in medical imaging: Recent advancements and future perspectives

    Kumari, S.; Singh, P . Deep learning for unsupervised domain adaptation in medical imaging: Recent advancements and future perspectives. Comput. Biol. Med. 2024, 170, 107912. https://doi.org/10.1016/j.compbiomed.2023.107912

    work page doi:10.1016/j.compbiomed.2023.107912 2024

  3. [3]

    Solving ill-posed inverse problems using iterative deep neural networks

    Adler, J.; Öktem, O. Solving ill-posed inverse problems using iterative deep neural networks. Inverse Probl. 2017, 33, 124007. https://doi.org/10.1088/1361-6420/aa9581

    work page doi:10.1088/1361-6420/aa9581 2017

  4. [4]

    Deep learning based unpaired image-to-image translation applications for medical physics: A systematic review

    Chen, J.; Chen, S.; Wee, L.; Dekker, A.; Bermejo, I. Deep learning based unpaired image-to-image translation applications for medical physics: A systematic review. Phys. Med. Biol. 2023, 68, 05TR01. https://doi.org/10.1088/1361-6560/acba74. https://doi.org/10.3390/tomography12040049 V ersion April 6, 2026 submitted to T omography 43 of 44

    work page doi:10.1088/1361-6560/acba74 2023

  5. [5]

    Memory-enhanced and multi-domain learning-based deep unrolling network for medical image reconstruction

    Jiang, H.; Zhang, Q.; Hu, Y .; Jin, Y .; Liu, H.; Chen, Z.; Zhao, Y .; Fan, W.; Zheng, H.; Liang, D.; et al. Memory-enhanced and multi-domain learning-based deep unrolling network for medical image reconstruction. Phys. Med. Biol. 2025, 70, 175008. https://doi.org/10.1088/1361-6560/adf939

    work page doi:10.1088/1361-6560/adf939 2025

  6. [6]

    Deep neural network-assisted improvement of quantum compressed sensing tomography

    Macarone-Palmieri, A.; Zambrano, L.; Lewenstein, M.; Acín, A.; Farina, D. Deep neural network-assisted improvement of quantum compressed sensing tomography . Phys. Scr. 2025, 100, 115106. https://doi.org/10.1088/1402-4896/ae1ada

    work page doi:10.1088/1402-4896/ae1ada 2025

  7. [7]

    Convex optimization algorithms in medical image reconstruction—In the age of AI

    Xu, J.; Noo, F. Convex optimization algorithms in medical image reconstruction—In the age of AI. Phys. Med. Biol. 2022, 67, 07TR01. https://doi.org/10.1088/1361-6560/ac3842

    work page doi:10.1088/1361-6560/ac3842 2022

  8. [8]

    Basis and current state of computed tomography perfusion imaging: A review

    Zeng, D.; Zeng, C.; Zeng, Z.; Li, S.; Deng, Z.; Chen, S.; Bian, Z.; Ma, J. Basis and current state of computed tomography perfusion imaging: A review. Phys. Med. Biol. 2022, 67, 18TR01. https://doi.org/10.1088/1361-6560/ac8717

    work page doi:10.1088/1361-6560/ac8717 2022

  9. [9]

    Algorithms in Tomography and Related Inverse ProblemsA Review

    Tassiopoulou, S.; Koukiou, G.; Anastassopoulos, V . Algorithms in Tomography and Related Inverse ProblemsA Review. Algo- rithms 2024, 17, 71. https://doi.org/10.3390/a17020071

    work page doi:10.3390/a17020071 2024

  10. [10]

    Physics-Informed Score-Based Diffusion Model for Limited-Angle Reconstruction of Cardiac Computed Tomography

    Han, S.; Xu, Y .; Wang, D.; Morovati, B.; Zhou, L.; Maltz, J.S.; Wang, G.; Yu, H. Physics-Informed Score-Based Diffusion Model for Limited-Angle Reconstruction of Cardiac Computed Tomography . IEEE T rans. Med Imaging 2025, 44, 3629–3640. https: //doi.org/10.1109/TMI.2024.3494271

    work page doi:10.1109/tmi.2024.3494271 2025

  11. [11]

    Anatomically Aided PET Image Reconstruction Using Deep Neural Networks

    Xie, Z.; Li, T.; Zhang, X.; Qi, W.; Asma, E. Anatomically Aided PET Image Reconstruction Using Deep Neural Networks. Med Phys. 2021, 48, 5244–5258. https://doi.org/10.1002/MP .15051

    work page doi:10.1002/mp 2021

  12. [12]

    Design of a digital phantom population for myocardial perfusion SPECT imaging research

    Ghaly , M.; Du, Y .; Fung, G.S.K.; Tsui, B.M.W.; Links, J.M.; Frey , E. Design of a digital phantom population for myocardial perfusion SPECT imaging research. Phys. Med. Biol. 2014, 59, 2935. https://doi.org/10.1088/0031-9155/59/12/2935

    work page doi:10.1088/0031-9155/59/12/2935 2014

  13. [13]

    A realistic phantom of the human head for PET-MRI

    Harries, J.; Jochimsen, T.H.; Scholz, T.; Schlender, T.; Barthel, H.; Sabri, O.; Sattler, B. A realistic phantom of the human head for PET-MRI. EJNMMI Phys. 2020, 7, 52. https://doi.org/10.1186/s40658-020-00320-z

    work page doi:10.1186/s40658-020-00320-z 2020

  14. [14]

    Design and construction of a realistic digital brain phantom

    Collins, D.; Zijdenbos, A.; Kollokian, V .; Sled, J.; Kabani, N.; Holmes, C.; Evans, A. Design and construction of a realistic digital brain phantom. IEEE T rans. Med Imaging 1998, 17, 463–468. https://doi.org/10.1109/42.712135

    work page doi:10.1109/42.712135 1998

  15. [15]

    Ground truth hardware phantoms for validation of diffusion-weighted MRI applications

    Pullens, P .; Roebroeck, A.; Goebel, R. Ground truth hardware phantoms for validation of diffusion-weighted MRI applications. J. Magn. Reson. Imaging (JMRI) 2010, 32, 482–488. https://doi.org/10.1002/jmri.22243

    work page doi:10.1002/jmri.22243 2010

  16. [16]

    Convergence study of an accelerated ML-EM algorithm using bigger step size

    Hwang, D.; Zeng, G.L. Convergence study of an accelerated ML-EM algorithm using bigger step size. Phys. Med. Biol. 2005, 51, 237. https://doi.org/10.1088/0031-9155/51/2/004

    work page doi:10.1088/0031-9155/51/2/004 2005

  17. [17]

    The Fourier reconstruction of a head section

    Shepp, L.A.; Logan, B.F. The Fourier reconstruction of a head section. IEEE T rans. Nucl. Sci. 1974, 21, 21–43. https://doi.org/ 10.1109/TNS.1974.6499235

    work page doi:10.1109/tns.1974.6499235 1974

  18. [18]

    2D & 3D Shepp-Logan Phantom Standards for MRI

    Gach, H.M.; Tanase, C.; Boada, F. 2D & 3D Shepp-Logan Phantom Standards for MRI. In Proceedings of the 2008 19th International Conference on Systems Engineering ; IEEE: New York, NY , USA, 2008; pp. 521–526. https://doi.org/10.1109/ICSEng.2008.15

    work page doi:10.1109/icseng.2008.15 2008

  19. [19]

    GATE: A simulation toolkit for PET and SPECT

    Jan, S.; Santin, G.; Strul, D.; Staelens, S.; Assié, K.; Autret, D.; Avner, S.; Barbier, R.; Bardiès, M.; Bloomfield, P .M.; et al. GATE: A simulation toolkit for PET and SPECT. Phys. Med. Biol. 2004, 49, 4543–4561. https://doi.org/10.1088/0031-9155/49/19/007

    work page doi:10.1088/0031-9155/49/19/007 2004

  20. [20]

    The OpenGATE ecosystem for Monte Carlo simulation in medical physics

    Sarrut, D.; Arbor, N.; Baudier, T.; Borys, D.; Etxebeste, A.; Fuchs, H.; Gajewski, J.; Grevillot, L.; Jan, S.; Kagadis, G.C.; et al. The OpenGATE ecosystem for Monte Carlo simulation in medical physics. Phys. Med. Biol. 2022, 67, 10.1088/1361–6560/ac8c83. https://doi.org/10.1088/1361-6560/ac8c83

    work page doi:10.1088/1361 2022

  21. [21]

    On the determination of functions from their integral values along certain manifolds

    Radon, J. On the determination of functions from their integral values along certain manifolds. IEEE T rans. Med Imaging 1986, 5, 170–176. https://doi.org/10.1109/TMI.1986.4307775

    work page doi:10.1109/tmi.1986.4307775 1986

  22. [22]

    De historiek van de tomografie [The history of tomography]

    Seynaeve, P .C.; Broos, J.I. De historiek van de tomografie [The history of tomography]. J. Belg. De Radiol. 1995, 78, 284–288

    work page 1995

  23. [23]

    Medical image registration

    Hill, D.L.G.; Batchelor, P .G.; Holden, M.; Hawkes, D.J. Medical image registration. Phys. Med. Biol. 2001, 46, R1–R45. https: //doi.org/10.1088/0031-9155/46/3/201

    work page doi:10.1088/0031-9155/46/3/201 2001

  24. [24]

    Correlation Coefficients: Appropriate Use and Interpretation,

    Schober, P .; Boer, C.; Schwarte, L.A. Correlation Coefficients: Appropriate Use and Interpretation. Anesth. Analg. 2018, 126, 1763–1768. https://doi.org/10.1213/ANE.0000000000002864

    work page doi:10.1213/ane.0000000000002864 2018

  25. [25]

    Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures

    Wang, Z.; Bovik, A.C. Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures. IEEE Signal Process. Mag. 2009, 26, 98–117. https://doi.org/10.1109/MSP .2008.930649

    work page doi:10.1109/msp 2009

  26. [26]

    Image Quality Metrics: PSNR vs

    Horé, A.; Ziou, D. Image Quality Metrics: PSNR vs. SSIM. In Proceedings of the 2010 20th International Conference on Pattern Recognition, Istanbul, T urkey; IEEE: New York, NY , USA, 2010; pp. 2366–2369. https://doi.org/10.1109/ICPR.2010.579

    work page doi:10.1109/icpr.2010.579 2010

  27. [27]

    Contrast-to-noise ratio (CNR) as a quality parameter in fMRI

    Geissler, A.; Gartus, A.; Foki, T.; Tahamtan, A.R.; Beisteiner, R.; Barth, M. Contrast-to-noise ratio (CNR) as a quality parameter in fMRI. J. Magn. Reson. Imaging (JMRI) 2007, 25, 1263–1270. https://doi.org/10.1002/jmri.20935

    work page doi:10.1002/jmri.20935 2007

  28. [28]

    A universal image quality index

    Wang, Z.; Bovik, A. A universal image quality index. IEEE Signal Process. Lett. 2002, 9, 81–84. https://doi.org/10.1109/97.995 823

    work page doi:10.1109/97.995 2002

  29. [29]

    Divergence measures based on the Shannon entropy

    Lin, J. Divergence measures based on the Shannon entropy . IEEE T rans. Inf. Theory 1991, 37, 145–151. https://doi.org/10.1109/ 18.61115

    work page 1991

  30. [30]

    A new metric for probability distributions

    Endres, D.; Schindelin, J. A new metric for probability distributions. IEEE T rans. Inf. Theory 2003, 49, 1858–1860. https: //doi.org/10.1109/TIT.2003.813506. https://doi.org/10.3390/tomography12040049 V ersion April 6, 2026 submitted to T omography 44 of 44

    work page doi:10.1109/tit.2003.813506 2003

  31. [31]

    On Information and Sufficiency

    Kullback, S.; Leibler, R.A. On Information and Sufficiency . Ann. Math. Stat. 1951, 22, 79–86. https://doi.org/10.1214/aoms/11 77729694

    work page doi:10.1214/aoms/11 1951

  32. [32]

    Asymptotic Methods in Statistical Decision Theory ; Springer Series in Statistics; Springer: New York, NY , USA, 1986

    Le Cam, L.M. Asymptotic Methods in Statistical Decision Theory ; Springer Series in Statistics; Springer: New York, NY , USA, 1986. https://doi.org/10.1007/978-1-4612-4946-7

    work page doi:10.1007/978-1-4612-4946-7 1986

  33. [33]

    Optimal T ransport: Old and New ; Grundlehren der Mathematischen Wissenschaften; Springer: Berlin/Heidelberg, Germany , 2009; V olume 338.https://doi.org/10.1007/978-3-540-71050-9

    Villani, C. Optimal T ransport: Old and New ; Grundlehren der Mathematischen Wissenschaften; Springer: Berlin/Heidelberg, Germany , 2009; V olume 338.https://doi.org/10.1007/978-3-540-71050-9

    work page doi:10.1007/978-3-540-71050-9 2009

  34. [34]

    Computational Optimal Transport: With Applications to Data Science

    Peyré, G.; Cuturi, M. Computational Optimal Transport: With Applications to Data Science. Found. T rends Mach. Learn. 2019, 11, 355–607. https://doi.org/10.1561/2200000073

    work page doi:10.1561/2200000073 2019

  35. [35]

    POT: Python Optimal Transport Library (Updated)

    Flamary , R.; Courty , N.; Gramfort, A.; Alaya, M.Z.; Boisbunon, A.; Chambon, S.; Chapel, L.; Corenflos, A.; Fatras, K.; Fournier, N.; et al. POT: Python Optimal Transport Library (Updated). J. Mach. Learn. Res. 2021, 22, 1–8. https://www.jmlr.org/papers/ v22/20-451.html

    work page 2021

  36. [36]

    Pulmonary Nodule Detection in CT Images: False Positive Reduction Using Multi-View Convolutional Networks

    Setio, A.A.A.; Ciompi, F.; Litjens, G.; Gerke, P .; Jacobs, C.; van Riel, S.J.; Wille, M.M.W.; Naqibullah, M.; Sánchez, C.I.; van Ginneken, B. Pulmonary Nodule Detection in CT Images: False Positive Reduction Using Multi-View Convolutional Networks. IEEE T rans. Med Imaging 2016, 35, 1160–1169. https://doi.org/10.1109/TMI.2016.2536809

    work page doi:10.1109/tmi.2016.2536809 2016

  37. [37]

    Region of interest analysis for fMRI

    Poldrack, R.A. Region of interest analysis for fMRI. Soc. Cogn. Affect. Neurosci. 2007, 2, 67–70. https://doi.org/10.1093/scan/ nsm006

    work page doi:10.1093/scan/ 2007

  38. [38]

    Region of Interest Coding Techniques for Medical Image Compression

    Doukas, C.; Maglogiannis, I. Region of Interest Coding Techniques for Medical Image Compression. IEEE Eng. Med. Biol. Mag. 2007, 26, 29–35. https://doi.org/10.1109/EMB.2007.901793

    work page doi:10.1109/emb.2007.901793 2007

  39. [39]

    Automatic and fast segmentation of breast region-of-interest (ROI) and density in MRIs

    Pandey , D.; Yin, X.; Wang, H.; Su, M.Y .; Chen, J.H.; Wu, J.; Zhang, Y . Automatic and fast segmentation of breast region-of-interest (ROI) and density in MRIs. Heliyon 2018, 4, e01042. https://doi.org/10.1016/j.heliyon.2018.e01042

    work page doi:10.1016/j.heliyon.2018.e01042 2018

  40. [40]

    Influence of region- of-interest determination on measurement of signal-to-noise ratio in liver on PET images

    Amakusa, S.; Matsuoka, K.; Kawano, M.; Hasegawa, K.; Ouchida, M.; Date, A.; Yoshida, T.; Sasaki, M. Influence of region- of-interest determination on measurement of signal-to-noise ratio in liver on PET images. Ann. Nucl. Med. 2018, 32, 1–6. https://doi.org/10.1007/s12149-017-1215-y

    work page doi:10.1007/s12149-017-1215-y 2018

  41. [41]

    Evaluation of Two Automated Methods for PET Region of Interest Analysis

    Schain, M.; Varnäs, K.; Cselényi, Z.; Halldin, C.; Farde, L.; Varrone, A. Evaluation of Two Automated Methods for PET Region of Interest Analysis. Neuroinformatics 2014, 12, 551–562. https://doi.org/10.1007/s12021-014-9233-6

    work page doi:10.1007/s12021-014-9233-6 2014

  42. [42]

    Regions of interest extraction from SPECT images for neural degeneration assessment using multimodality image fusion

    Jiang, C.F.; Chang, C.C.; Huang, S.H. Regions of interest extraction from SPECT images for neural degeneration assessment using multimodality image fusion. Multidimens. Syst. Signal Process. 2012, 23, 437–449. https://doi.org/10.1007/s11045-011-0 162-3

    work page doi:10.1007/s11045-011-0 2012

  43. [43]

    Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography

    Gordon, R.; Bender, R.; Herman, G.T. Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography . J. Theor. Biol. 1970, 29, 471–481. https://doi.org/10.1016/0022-5193(70)90109-8

    work page doi:10.1016/0022-5193(70)90109-8 1970

  44. [44]

    Fundamentals of Computerized T omography: Image Reconstruction from Projections , 2nd ed.; Springer: Berlin/Heidelberg, Germany , 2009

    Herman, G.T. Fundamentals of Computerized T omography: Image Reconstruction from Projections , 2nd ed.; Springer: Berlin/Heidelberg, Germany , 2009

    work page 2009

  45. [45]

    Maximum Likelihood Reconstruction for Emission Tomography .IEEE T rans

    Shepp, L.A.; Vardi, Y . Maximum Likelihood Reconstruction for Emission Tomography .IEEE T rans. Med Imaging1982, 1, 113–122. https://doi.org/10.1109/TMI.1982.4307558

    work page doi:10.1109/tmi.1982.4307558 1982

  46. [46]

    A Novel Analysis Method for Emission Tomography

    Papanicolas, C.N.; Koutsantonis, L.; Stiliaris, E. A Novel Analysis Method for Emission Tomography . arXiv 2018, arXiv:1804.03915. https://doi.org/10.48550/arXiv .1804.03915

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv 2018

  47. [47]

    In: 2021 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), Piscataway, NJ, USA, pp

    Keliri, A.; Koutsantonis, L.; Stiliaris, E.; Parpottas, Y .; Charitou, G.; Panagi, S.; Papanicolas, C.N. Application of RISE in SPECT Myocardial Perfusion Imaging, using a Cardiac Phantom. In Proceedings of the 2021 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC); IEEE: New York, NY , USA, 2021; pp. 1–5. https://doi.org/10.1109/NSS...

    work page doi:10.1109/nss/mic44867.2021.987592 2021

  48. [48]

    Examining an image reconstruction method in infrared emission tomography

    Koutsantonis, L.; Rapsomanikis, A.N.; Stiliaris, E.; Papanicolas, C.N. Examining an image reconstruction method in infrared emission tomography . Infrared Phys. T echnol. 2019, 98, 266–277. https://doi.org/10.1016/j.infrared.2019.03.015

    work page doi:10.1016/j.infrared.2019.03.015 2019

  49. [49]

    RISE: Tomographic Image Reconstruction in Positron Emission Tomography

    Lemesios, C.; Koutsantonis, L.; Papanicolas, C.N. RISE: Tomographic Image Reconstruction in Positron Emission Tomography . In Proceedings of the 2019 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) ; IEEE: New York, NY , USA, 2019; pp. 1–4. https://doi.org/10.1109/NSS/MIC42101.2019.9060020

    work page doi:10.1109/nss/mic42101.2019.9060020 2019

  50. [50]

    Delete-m Jackknife for Unequal m

    Busing, F.M.T.A.; Meijer, E.; van der Leeden, R. Delete-m Jackknife for Unequal m. Stat. Comput. 1999, 9, 3–8. https: //doi.org/10.1023/A:1008800423698

    work page doi:10.1023/a:1008800423698 1999

  51. [51]

    Notes on Bias in Estimation

    Quenouille, M.H. Notes on Bias in Estimation. Biometrika 1956, 43, 353–360. https://doi.org/10.2307/2332914

    work page doi:10.2307/2332914 1956

  52. [52]

    Bias and confidence in notquite large samples

    Tukey , J.W. Bias and confidence in notquite large samples. Ann. Math. Stat. 1958, 29, 614. https://doi.org/10.1214/aoms/1177 706647. Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) dis...

    work page doi:10.1214/aoms/1177 1958