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arxiv: 2510.23317 · v3 · submitted 2025-10-27 · 📡 eess.IV

Equivariance2Inverse: A Practical Self-Supervised CT Reconstruction Method Benchmarked on Real, Limited-Angle, and Blurred Data

Dirk Elias Schut , Adriaan Graas , Robert van Liere , Tristan van Leeuwen This is my paper

Pith reviewed 2026-05-18 03:21 UTC · model grok-4.3

classification 📡 eess.IV
keywords self-supervised learningCT reconstructionlimited-angle tomographyequivariant imagingscintillator blurartifact reductioninverse problems
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The pith

Equivariance2Inverse reconstructs CT images from limited-angle and blurred scans without ground truth by using rotational invariance.

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

This paper introduces Equivariance2Inverse, a self-supervised method for reconstructing X-ray CT images that avoids the need for ground-truth training pairs. It reviews assumptions in existing self-supervised approaches and combines Robust Equivariant Imaging with Sparse2Inverse to create a method tolerant to scintillator blurring and limited scanning angles. The benchmark on real 2DeteCT data and synthetic phantoms demonstrates that pixel-independent noise assumptions break down with blurring, while rotational invariance of object distributions helps suppress artifacts in limited-angle cases. This makes the approach more practical for real-world CT applications where full data or clean labels are unavailable.

Core claim

The authors propose Equivariance2Inverse, which integrates equivariance under rotations into a self-supervised inverse problem framework to jointly address noise modeling inaccuracies and angular undersampling in CT reconstruction.

What carries the argument

The equivariance loss based on rotating the reconstructed object and enforcing consistency, combined with sparsity-promoting regularization in the inverse mapping.

If this is right

  • Methods assuming independent pixel noise perform poorly on data affected by scintillator blurring.
  • Rotational invariance of the object distribution can be leveraged to reduce artifacts when scanning angles are limited.
  • The combined Equivariance2Inverse method shows improved robustness on both real experimental datasets and controlled synthetic tests.
  • Self-supervised reconstruction benefits from explicitly accounting for mismatches in the forward imaging model such as blurring.

Where Pith is reading between the lines

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

  • This symmetry-based approach might generalize to other tomographic modalities that exhibit rotational symmetries in their object classes.
  • Future work could test the method on clinical datasets with varying degrees of rotational invariance to identify domain-specific limitations.
  • Combining the equivariance loss with more detailed models of detector response could yield further gains in reconstruction quality.

Load-bearing premise

The scanned objects come from a distribution that is sufficiently rotationally invariant for the equivariance constraint to guide the reconstruction without adding new errors.

What would settle it

A test set consisting of objects with strong preferred orientations, such as elongated structures all aligned in one direction, where applying the rotational equivariance would degrade the reconstruction quality instead of improving it.

Figures

Figures reproduced from arXiv: 2510.23317 by Adriaan Graas, Dirk Elias Schut, Robert van Liere, Tristan van Leeuwen.

Figure 1
Figure 1. Figure 1: Example of scintillator blur in the 2DeteCT dataset. Each horizontal [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of how the loss is calculated in the self-supervised CT reconstruction methods. The arrows with letters correspond to function calls or [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The test-set PSNR of neural networks trained with different values [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A reconstruction from each method on the first image of the test set of each dataset. The insets provide a two times magnified view of the center-left [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

Deep learning has shown impressive results in reducing noise and artifacts in X-ray computed tomography (CT) reconstruction. Self-supervised CT reconstruction methods are especially appealing for real-world applications because they require no ground truth training examples. However, these methods involve a simplified X-ray physics model during training, which may make inaccurate assumptions, for example, about scintillator blurring, the scanning geometry, or the distribution of the noise. As a result, they can be less robust to real-world imaging circumstances. In this paper, we review the model assumptions of six recent self-supervised CT reconstruction methods. Based on this, we combined concepts of the Robust Equivariant Imaging and Sparse2Inverse methods in a new self-supervised CT reconstruction method called Equivariance2Inverse that is robust to scintillator blurring and limited-angle data. We benchmarked Equivariance2Inverse and the existing methods on the real-world 2DeteCT dataset and on synthetic data with and without scintillator blurring and a limited-angle scanning geometry. The results of our benchmark show that methods that assume that the noise is pixel-wise independent do not perform well on data with scintillator blurring. Moreover, they show that when the distribution of objects is rotationally invariant, this invariance can be used to reduce artifacts in limited-angle reconstructions.

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

1 major / 2 minor

Summary. The paper proposes Equivariance2Inverse, a self-supervised CT reconstruction method formed by combining Robust Equivariant Imaging (to enforce rotational equivariance) with Sparse2Inverse (to handle limited-angle data). It reviews the modeling assumptions of six recent self-supervised methods, then benchmarks the new method together with the others on the real 2DeteCT dataset and on controlled synthetic phantoms with and without scintillator blurring and limited-angle geometries. The central empirical claims are that methods assuming pixel-wise independent noise degrade on blurred data and that, when the object distribution is rotationally invariant, the equivariance loss reduces limited-angle artifacts.

Significance. If the benchmark results are reproducible and the rotational-invariance premise holds for the target domains, the work supplies a practical, self-supervised baseline for real-world CT reconstruction under non-ideal conditions (blurring, limited angles) and supplies a useful comparative study of modeling assumptions. The explicit conditioning of the artifact-reduction claim on rotational invariance of p(x) is a strength that makes the result falsifiable.

major comments (1)
  1. Abstract and §4 (benchmark description): the claim that rotational invariance 'can be used to reduce artifacts' is load-bearing for the performance advantage of Equivariance2Inverse over the other five methods, yet no quantitative check (e.g., empirical rotational variance of the 2DeteCT or phantom distributions, or an ablation with deliberately orientation-biased data) is reported. Without such a test the equivariance loss could penalize valid structure and introduce new artifacts precisely when the premise fails.
minor comments (2)
  1. Abstract: no numerical metrics, error bars, or table references are given, which is acceptable for an abstract but makes the magnitude of improvement impossible to gauge from the summary alone.
  2. Method section: the weighting between the equivariance loss and the sparsity term is listed among the free parameters; a sensitivity plot or recommended default values would improve reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and the insightful major comment. We respond point-by-point below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: Abstract and §4 (benchmark description): the claim that rotational invariance 'can be used to reduce artifacts' is load-bearing for the performance advantage of Equivariance2Inverse over the other five methods, yet no quantitative check (e.g., empirical rotational variance of the 2DeteCT or phantom distributions, or an ablation with deliberately orientation-biased data) is reported. Without such a test the equivariance loss could penalize valid structure and introduce new artifacts precisely when the premise fails.

    Authors: We agree that a quantitative verification of the rotational-invariance assumption would strengthen the presentation. The manuscript already states the claim conditionally ('when the distribution of objects is rotationally invariant'), but we did not report an explicit metric such as average rotational variance across the 2DeteCT slices or an ablation on orientation-biased phantoms. In the revised manuscript we will add a short subsection in §4 that computes a simple rotational-variance statistic (mean absolute difference between an image and its 90-degree rotations, averaged over the test set) for both the real 2DeteCT data and the synthetic phantoms. We will also note that the observed gains of Equivariance2Inverse remain consistent with the assumption holding reasonably well for the object classes present in these datasets. We do not plan to add a full ablation on deliberately biased data, as that would shift the paper’s focus away from real-world applicability; however, we will briefly discuss the risk that the equivariance loss could penalize valid structure when the premise fails. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical benchmarking of combined self-supervised methods

full rationale

The paper reviews assumptions in prior self-supervised CT methods, proposes Equivariance2Inverse by combining Robust Equivariant Imaging with Sparse2Inverse, and evaluates via benchmarking on real 2DeteCT data plus synthetic cases with/without blurring and limited angles. The rotational invariance of the object distribution is stated as a domain condition under which the equivariance loss can reduce artifacts, not derived from the model equations or fitted to the target result. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or renamed input; results are external benchmarks against real and synthetic data. This is the common honest finding for a methods-plus-benchmark paper.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The method inherits standard assumptions from deep-learning CT reconstruction (differentiable forward model, approximate noise statistics) plus two domain assumptions: rotational invariance of the object distribution and that scintillator blur can be treated as a fixed degradation rather than learned jointly.

free parameters (2)
  • equivariance loss weight
    Hyperparameter balancing the rotation-equivariance term against the data-consistency term; value not stated in abstract.
  • sparsity regularization strength
    Inherited from Sparse2Inverse; controls how strongly the reconstruction favors sparse representations.
axioms (2)
  • domain assumption The forward imaging model (including scintillator blur) is known and differentiable.
    Required for the self-supervised loss; stated as a review of model assumptions in the abstract.
  • domain assumption Object distribution is approximately rotationally invariant.
    Invoked to justify use of equivariant imaging for limited-angle artifact reduction.

pith-pipeline@v0.9.0 · 5781 in / 1513 out tokens · 22095 ms · 2026-05-18T03:21:04.596599+00:00 · methodology

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Forward citations

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    D. E. Schut, “Synthetically generated foam ct dataset,” 2025. [Online]. Available: https://doi.org/10.5281/zenodo.16735632 Dirk Elias Schutis a PhD researcher at the Compu- tational Imaging group of the Centrum Wiskunde & Informatica (CWI) in the Netherlands. His research is part of the UTOPIA project on bringing per product CT imaging for quality control...

    work page doi:10.5281/zenodo.16735632 2025