pith. machine review for the scientific record. sign in

arxiv: 2604.23675 · v1 · submitted 2026-04-26 · 📡 eess.IV · cs.CV· physics.med-ph

Recognition: unknown

GS-DOT: Gaussian splatting-based image reconstruction for diffuse optical tomography

Jingjing Jiang

Authors on Pith no claims yet

Pith reviewed 2026-05-08 04:58 UTC · model grok-4.3

classification 📡 eess.IV cs.CVphysics.med-ph
keywords Gaussian splattingdiffuse optical tomographyimage reconstructionabsorption mappingphoton diffusiontime-resolved measurementsoptimizationsynthetic validation
0
0 comments X

The pith

Absorption maps in scattering tissue are reconstructed by optimizing a sparse set of anisotropic Gaussian primitives to match time-resolved light measurements under diffusion transport.

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

The paper establishes that Gaussian splatting can be repurposed for diffuse optical tomography by replacing ray-based rendering with diffusion approximations for light propagation in turbid media. Absorption is expressed as a sum of a few anisotropic Gaussian shapes whose parameters are adjusted through analytic gradients and the Adam optimizer to reproduce measured point-spread functions. Validation on synthetic tissue phantoms shows precise recovery of absorber locations and strengths, even when the input signals contain noise, together with substantially lower memory consumption than conventional voxel-based approaches. A reader would care because DOT is used for non-invasive functional imaging of biological tissues, and an efficient reconstruction technique could make the modality more practical for applications such as breast or brain imaging.

Core claim

GS-DOT represents the unknown absorption distribution as a sparse collection of anisotropic Gaussian primitives and optimizes their positions, sizes, orientations, and amplitudes so that the resulting diffusion-modeled light transport matches the measured time-resolved data, achieving accurate localization and quantification on synthetic models while demonstrating noise robustness and reduced memory demand.

What carries the argument

Sparse anisotropic Gaussian primitives whose parameters are updated by Adam optimization using analytic gradients derived from the photon diffusion equation instead of ray transport.

If this is right

  • Accurate recovery of absorber position and strength holds for both clean and noisy synthetic measurements.
  • Memory usage drops dramatically relative to dense voxel grids.
  • The same primitive representation supports time-resolved data without explicit ray tracing.
  • Localization remains reliable when the underlying tissue scattering is modeled by the diffusion approximation.

Where Pith is reading between the lines

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

  • The approach could be tested on experimental phantom or in-vivo data to check whether the Gaussian basis still suffices when the forward model contains additional uncertainties.
  • Extending the primitives to three-dimensional distributions would allow direct comparison against existing 3D DOT algorithms.
  • If the optimization converges reliably, the method might support real-time or low-power hardware implementations of DOT.
  • Hybrid schemes that combine a few Gaussian primitives with a low-resolution background grid could address cases where the absorption field is too complex for a purely sparse representation.

Load-bearing premise

A small number of anisotropic Gaussian shapes can faithfully represent arbitrary absorption patterns inside scattering tissue and the optimizer will reach the global solution rather than a poor local minimum.

What would settle it

Reconstruction of a known, highly irregular absorption distribution that cannot be approximated well by any modest number of Gaussians, measured by large errors in both location and amplitude even after full optimization on clean data.

Figures

Figures reproduced from arXiv: 2604.23675 by Jingjing Jiang.

Figure 1
Figure 1. Figure 1: Measurement geometry. Ten source and ten detector optodes are distributed view at source ↗
Figure 2
Figure 2. Figure 2: GS-DOT reconstruction results for four test cases. view at source ↗
read the original abstract

This work presents GS-DOT, a novel image reconstruction framework based on Gaussian Splatting (GS) for diffuse optical tomography (DOT). Inspired by GS for rendering applications, absorption coefficients are represented as a sparse sum of anisotropic Gaussian primitives optimized to fit measured time-resolved point-spread functions through analytic gradients and Adam optimization. This is the first adaptation of GS algorithms in the photon diffusion regime, where the ray transport function is replaced by the diffusion functions to enable accurate modeling of light transport in highly scattering media. Validation on synthetic tissue models demonstrate high accuracy in localization and quantification of reconstructed absorption maps for both clean and noisy signals. GS-DOT has demonstrated high robustness to noise and showed a huge reduction in memory demand.

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

3 major / 2 minor

Summary. The manuscript introduces GS-DOT, a novel image reconstruction method for diffuse optical tomography that adapts Gaussian splatting by representing the absorption coefficient as a sparse sum of anisotropic Gaussian primitives. These parameters are optimized via the Adam algorithm using analytic gradients computed through the diffusion approximation forward model applied to time-resolved point-spread function measurements. The authors claim this is the first such adaptation to the photon diffusion regime and report that synthetic tissue model experiments demonstrate high accuracy in localization and quantification, robustness to noise, and substantial memory reduction.

Significance. If the central claims are substantiated with rigorous quantitative evidence, the work would offer a memory-efficient, differentiable alternative to traditional voxel- or mesh-based DOT reconstructions, potentially scaling to larger domains or enabling faster iterations. The replacement of ray-transport functions with diffusion kernels represents a genuine technical extension of Gaussian splatting into scattering media and could seed similar differentiable-rendering approaches in other optical inverse problems.

major comments (3)
  1. [Abstract] Abstract: the claims of 'high accuracy in localization and quantification' and 'huge reduction in memory demand' are unsupported by any numerical metrics, baseline comparisons (e.g., against finite-element or iterative voxel methods), number of Gaussians employed, or convergence statistics; without these the strength of the validation cannot be assessed.
  2. [Method] Method section (representation and optimization): the load-bearing assumption that an arbitrary absorption distribution inside scattering tissue can be accurately recovered as a sparse sum of anisotropic Gaussians is not tested for cases containing sharp boundaries, disconnected regions, or fine-scale structure; because the representation is smooth by construction, reconstruction error is guaranteed to increase for such phantoms even if Adam converges.
  3. [Validation] Validation section: no details are provided on the specific synthetic tissue models, the exact number of Gaussian primitives, noise levels, convergence behavior, or statistical analysis (error bars, multiple random initializations); the reported robustness therefore cannot be verified or reproduced.
minor comments (2)
  1. [Method] Clarify the precise mathematical substitution of the diffusion Green's function for the ray-transport function, ideally with an explicit equation reference.
  2. [Results] Results figures should include quantitative error maps, memory-usage tables, and direct side-by-side comparisons with at least one standard DOT solver.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on our manuscript. We address each of the major comments below and indicate the revisions we have made or will make to strengthen the paper.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claims of 'high accuracy in localization and quantification' and 'huge reduction in memory demand' are unsupported by any numerical metrics, baseline comparisons (e.g., against finite-element or iterative voxel methods), number of Gaussians employed, or convergence statistics; without these the strength of the validation cannot be assessed.

    Authors: We agree that the abstract would benefit from including specific quantitative metrics to support our claims. In the revised version, we will update the abstract to include key numerical results from our experiments, such as localization and quantification errors, memory reduction factors compared to voxel-based methods, and the number of Gaussian primitives used. These will be supported by the detailed results in the validation section, and we will incorporate baseline comparisons to traditional methods where possible. revision: yes

  2. Referee: [Method] Method section (representation and optimization): the load-bearing assumption that an arbitrary absorption distribution inside scattering tissue can be accurately recovered as a sparse sum of anisotropic Gaussians is not tested for cases containing sharp boundaries, disconnected regions, or fine-scale structure; because the representation is smooth by construction, reconstruction error is guaranteed to increase for such phantoms even if Adam converges.

    Authors: The referee raises a valid point regarding the limitations of the Gaussian representation for non-smooth distributions. Our current validation focuses on phantoms with localized inclusions that can be well-approximated by Gaussians, which are common in DOT applications. However, we acknowledge that for phantoms with sharp boundaries or fine-scale structures, the smooth nature of Gaussians may lead to increased error. In the revision, we will add a discussion of this limitation and include additional experiments with phantoms featuring disconnected regions and sharper features, using a larger number of primitives to better approximate such structures. We will report the reconstruction errors for these cases to provide a more complete assessment. revision: partial

  3. Referee: [Validation] Validation section: no details are provided on the specific synthetic tissue models, the exact number of Gaussian primitives, noise levels, convergence behavior, or statistical analysis (error bars, multiple random initializations); the reported robustness therefore cannot be verified or reproduced.

    Authors: We apologize for the lack of sufficient detail in the validation section, which hinders reproducibility. The revised manuscript will expand this section to include: detailed descriptions of the synthetic tissue models (geometry, background and inclusion optical properties), the exact number of Gaussian primitives optimized in each experiment, the noise levels applied (e.g., additive Gaussian noise with standard deviations corresponding to 1%, 5%, and 10% of signal amplitude), convergence plots or statistics (e.g., loss vs. iterations), and statistical analysis with error bars from at least 5 random initializations per phantom. This will allow readers to verify the reported robustness to noise. revision: yes

Circularity Check

0 steps flagged

No circularity: parameterization and optimization are independent of target quantities

full rationale

The paper parameterizes absorption maps as a sum of anisotropic Gaussians and optimizes their parameters by minimizing a loss against measured time-resolved data under the diffusion forward model. This is a standard inverse-problem formulation; the recovered map is not defined by the same quantities it is claimed to predict, nor does any load-bearing step reduce to a self-citation or ansatz imported from the authors' prior work. Validation on synthetic phantoms is presented as an external check rather than a tautology. No quoted equation or claim exhibits the forbidden reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is limited to the core modeling assumption stated in the text.

axioms (1)
  • domain assumption The diffusion approximation accurately describes light transport in highly scattering media.
    Invoked when the paper replaces the ray transport function with diffusion functions for the GS adaptation.

pith-pipeline@v0.9.0 · 5411 in / 1324 out tokens · 77419 ms · 2026-05-08T04:58:59.997987+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

30 extracted references

  1. [1]

    Optical tomography: forward and inverse problems,

    S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl.25(2009)

    2009

  2. [2]

    Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,

    H. Dehghani, M. E. Eames, P. K. Yalavarthy,et al., “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Commun. numerical methods engineering25, 711–732 (2009)

    2009

  3. [3]

    Image reconstruction for novel time domain near infrared optical tomography: towards clinical applications,

    J. Jiang, A. Di Costanzo Mata, S. Lindner,et al., “Image reconstruction for novel time domain near infrared optical tomography: towards clinical applications,” Biomed. Opt. Express11, 4723–4734 (2020)

    2020

  4. [4]

    Deep learning based image reconstruction for diffuse optical tomography,

    H. Ben Yedder, A. BenTaieb, M. Shokoufi,et al., “Deep learning based image reconstruction for diffuse optical tomography,” inInternational workshop on machine learning for medical image reconstruction,(Springer, 2018), pp. 112–119

    2018

  5. [5]

    When does the diffusion approximation fail to describe photon transport in random media?

    K. Yoo, F. Liu, and R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. review letters64, 2647 (1990)

    1990

  6. [6]

    Machinelearningmodelwithphysicalconstraintsfordiffuseopticaltomography,

    Y.Zou,Y.Zeng,S.Li,andQ.Zhu,“Machinelearningmodelwithphysicalconstraintsfordiffuseopticaltomography,” Biomed. optics express12, 5720–5735 (2021)

    2021

  7. [7]

    A modular deep learning-based approach for diffuse optical tomography reconstruction,

    A. Benfenati, P. Causin, and M. Quinteri, “A modular deep learning-based approach for diffuse optical tomography reconstruction,” Numer. Funct. Anal. Optim. pp. 1–33 (2025)

    2025

  8. [8]

    Elastic net regularization in diffuse optical tomography applications,

    P. Causin, G. Naldi, and R.-M. Weishaeupl, “Elastic net regularization in diffuse optical tomography applications,” in 2019 IEEE 16th international symposium on biomedical imaging (ISBI 2019),(IEEE, 2019), pp. 1627–1630

    2019

  9. [9]

    Regularizationtechniquesforinverseproblemindotapplications,

    A.Benfenati,P.Causin,M.Lupieri,andG.Naldi,“Regularizationtechniquesforinverseproblemindotapplications,” inJournal of physics: conference series,vol. 1476 (IOP Publishing, 2020), p. 012007

    2020

  10. [10]

    Inexact bregman iteration with an application to poisson data reconstruction,

    A. Benfenati and V. Ruggiero, “Inexact bregman iteration with an application to poisson data reconstruction,” Inverse Probl.29, 065016 (2013)

    2013

  11. [11]

    3d gaussian splatting for real-time radiance field rendering,

    B. Kerbl, G. Kopanas, T. Leimkühler, and G. Drettakis, “3d gaussian splatting for real-time radiance field rendering,” (2023)

    2023

  12. [12]

    Radiative gaussian splatting for efficient x-ray novel view synthesis,

    Y. Cai, Y. Liang, J. Wang,et al., “Radiative gaussian splatting for efficient x-ray novel view synthesis,” (2024)

    2024

  13. [13]

    Resolution and penetration depth of reflection-mode time-domain near infrared optical tomography using a tof spad camera,

    J. Jiang, M. Ackermann, E. Russomanno,et al., “Resolution and penetration depth of reflection-mode time-domain near infrared optical tomography using a tof spad camera,” Biomed. Opt. Express13, 6711–6723 (2022)

    2022

  14. [14]

    Dynamic time domain near-infrared optical tomography based on a spad camera,

    J. Jiang, A. Di Costanzo Mata, S. Lindner,et al., “Dynamic time domain near-infrared optical tomography based on a spad camera,” Biomed. Opt. Express11, 5470–5477 (2020)

    2020

  15. [15]

    Mri-guided optical tomography: prospects and computation for a new imaging method,

    R. L. Barbour, H. L. Graber, Jenghwa Chang,et al., “Mri-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng.2, 63–77 (1995)

    1995

  16. [16]

    Fast reconstruction of optical properties for complex segmentations in near infrared imaging,

    J. Jiang, M. Wolf, and S. S. Majos, “Fast reconstruction of optical properties for complex segmentations in near infrared imaging,” J. Mod. Opt.64, 732–742 (2017)

    2017

  17. [17]

    A new method based on virtual fluence detectors and software toolbox for handheld spectral optoacoustic tomography,

    J. Jiang, A. Kalyanov, L. Ahnen,et al., “A new method based on virtual fluence detectors and software toolbox for handheld spectral optoacoustic tomography,” Adv Exp Med Biol1072, 357–361 (2018)

    2018

  18. [18]

    Discrimination of complex activation patterns in near infrared optical tomography with artificial neural networks,

    J. Jiang, L. Ahnen, S. Lindner,et al., “Discrimination of complex activation patterns in near infrared optical tomography with artificial neural networks,” Adv Exp Med Biol1072, 313–318 (2018)

    2018

  19. [19]

    Multimodal imaging combining time-domain near-infrared optical tomography and continuous-wave fluorescence molecular tomography,

    W. Ren, J. Jiang, A. Di Costanzo Mata,et al., “Multimodal imaging combining time-domain near-infrared optical tomography and continuous-wave fluorescence molecular tomography,” Opt. Express28, 9860–9874 (2020)

    2020

  20. [20]

    A comprehensive overview of diffuse correlation spectroscopy: Theoretical framework, recent advances in hardware, analysis, and applications,

    Q. Wang, M. Pan, L. Kreiss,et al., “A comprehensive overview of diffuse correlation spectroscopy: Theoretical framework, recent advances in hardware, analysis, and applications,” NeuroImage298, 120793 (2024)

    2024

  21. [21]

    Electricalimpedancetomography-recentapplicationsanddevelopments,

    S.Mansouri,Y.Alharbi,F.Haddad,et al.,“Electricalimpedancetomography-recentapplicationsanddevelopments,” J Electr Bioimpedance12, 50–62 (2021)

    2021

  22. [22]

    Optical tomography in medical imaging,

    S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl.15, R41–R93 (1999)

    1999

  23. [23]

    Radiative transfer in two-dimensional infinitely extended scattering media,

    A. Liemert and A. Kienle, “Radiative transfer in two-dimensional infinitely extended scattering media,” J. Phys. A: Math. Theor.44, 505206 (2011)

    2011

  24. [24]

    Time-resolved optical tomography,

    J. C. Hebden and K. Wong, “Time-resolved optical tomography,” Appl. optics32, 372–380 (1993)

    1993

  25. [25]

    Diffuse optics for tissue monitoring and tomography,

    T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Reports on progress physics73, 076701 (2010)

    2010

  26. [26]

    Adam: A method for stochastic optimization,

    D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” (2017)

    2017

  27. [27]

    Refractive index of biological tissues: Review, measurement techniques, and applications,

    R. Khan, B. Gul, S. Khan,et al., “Refractive index of biological tissues: Review, measurement techniques, and applications,” Photodiagnosis Photodyn. Ther.33, 102192 (2021)

    2021

  28. [28]

    Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,

    H. Dehghani, M. E. Eames, P. K. Yalavarthy,et al., “Near infrared optical tomography using nirfast: Algorithm for numerical model and image reconstruction,” Commun Numer Methods Eng25, 711–732 (2008)

    2008

  29. [29]

    Monte carlo simulation of photon migration in 3d turbid media accelerated by graphics processing units,

    Q. Fang and D. A. Boas, “Monte carlo simulation of photon migration in 3d turbid media accelerated by graphics processing units,” Opt Express17, 20178–90 (2009)

    2009

  30. [30]

    Thetoast++softwaresuiteforforwardandinversemodelinginopticaltomography,

    M.SchweigerandS.R.Arridge,“Thetoast++softwaresuiteforforwardandinversemodelinginopticaltomography,” J. biomedical optics19, 040801 (2014)

    2014