Plug-and-Play with 2.5D Artifact Reduction Prior for Fast and Accurate Industrial Computed Tomography Reconstruction

Amirkoushyar Ziabari; Aniket Pramanik; Haley Duba-Sullivan; Venkatakrishnan Singanallur

REVIEW 4 major objections 3 minor 47 references

Plug-and-Play with 2.5D Artifact Reduction Prior for Fast and Accurate Industrial Computed Tomography Reconstruction

T0 review · 4 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Upgrading the artifact-reduction prior from 2D to 2.5D improves sparse-view cone-beam XCT reconstruction, preserves fine pore structure, and suppresses beam hardening directly during reconstruction.

desk verdict A fair, honest 2.5D-versus-2D A/B in PnP XCT reconstruction; the only real weakness is that accuracy is measured against reconstructed references when known CAD ground truth exists. read the letter →

arxiv 2506.14719 v1 pith:CA2DBR2T submitted 2025-06-17 eess.IV cs.CV

Haley Duba-Sullivan , Aniket Pramanik , Venkatakrishnan Singanallur , Amirkoushyar Ziabari This is my paper · ORCID

classification eess.IVcs.CV

keywords X-raycomputedtomographyplug-and-playreconstructionartifactreductionprior2.5DCNNbeamhardeningsparse-viewCTdefectdetectionsuper-resolution

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

Industrial cone-beam X-ray computed tomography needs many projections to produce high-quality 3D reconstructions, making scans slow and expensive. This paper argues that placing a 2.5D artifact-reduction CNN inside a plug-and-play reconstruction framework recovers near-reference quality from sparse, noisy, beam-hardened scans: the network sees five adjacent slices at once, using inter-slice context to clean the center slice while staying as cheap as a 2D model. The authors show that this 2.5D prior outperforms the 2D prior it extends, preserving fine pore shape and boosting defect-detection recall and precision, and that it removes beam-hardening artifacts inside the reconstruction so no separate artifact-correction preprocessing is needed. They also demonstrate that a prior trained only on synthetic scans reconstructs experimental aluminum-cerium parts well, which matters because deep-learned CT models typically fail on out-of-distribution data.

What carries the argument

The load-bearing mechanism is the alternating-minimization PnP loop with a quadratic-penalty variable split: a data-fidelity step (conjugate gradient on the cone-beam forward model) alternates with a regularization step in which the proximal operator is replaced by a 2.5D artifact-reduction UNet. The 2.5D network takes five adjacent slices as input channels and is trained with an L1 residual loss to output the cleaned center slice, giving it volumetric context at 2D memory cost; an adaptive grid search on center-slice quality sets the penalty parameter β each iteration. This combination lets the reconstruction suppress noise, cupping and streak artifacts from beam hardening, and view-sparsity artifacts while preserving pore boundaries.

What would settle it

Recompute the experimental comparison using a reference obtained from a materially denser acquisition (for example, thousands of views at high signal) or a known ground-truth phantom, and test whether the 2.5D PnP advantage in recall and precision over 2D PnP survives; if it shrinks or reverses, the reported gains were partly matching reference artifacts instead of true pore structure.

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Extended reading notes

Core claim

The paper claims that upgrading the artifact-reduction prior in a plug-and-play (PnP) reconstruction scheme from 2D to 2.5D yields a clear improvement in sparse-view cone-beam XCT. In the PnP loop, the regularization sub-problem is solved by a CNN trained to map low-quality FDK inputs (few views, Poisson-like noise, beam hardening) to dense-view artifact-free targets; the 2.5D version feeds a stack of five neighboring slices and predicts the residual for the center slice. The authors report lower NRMSE and higher SSIM on synthetic in-distribution and most out-of-distribution tests, higher recall and precision for 75–125 µm flaws, and visible recovery of pores that 2D PnP distorts or misses. On experimental 145-view scans, the 2.5D model trained entirely on synthetic data matches or beats the 2D prior on task-specific defect detection and achieves the highest SNR and CNR, at essentially the same runtime (about 48 minutes per 1356×1356×1264 volume on four GPUs) as 2D PnP and far below MBIR.

Load-bearing premise

The results assume that the reference reconstructions used for training and evaluation — a dense-view fast analytic reconstruction with a single-energy beam on synthetic data, and a slower iterative reconstruction on experimental data — faithfully represent the true object rather than carrying their own residual artifacts.

Editorial extensions

If this is right

Sparse-view industrial scans could be cut to 73–145 views and still yield defect-detection-quality volumes, with beam hardening handled inside reconstruction rather than as a preprocessing step.
Large-volume reconstruction time and memory drop by an order of magnitude versus MBIR (about 48 minutes and 35 GB on four GPUs, compared with about 6 hours and 300 GB), making high-quality XCT feasible for routine inspection.
A synthetic-only training recipe transfers to experimental parts, so new materials and geometries may not require experimental ground-truth training data.
Out-of-distribution noise levels (up to four times the training noise) degrade gracefully, while extreme view sparsity (73 views) still exposes a sensitivity and false-positive trade-off.

Reading between the lines

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

Because the 2.5D prior leverages inter-slice consistency, the same architecture could plausibly suppress other volumetric artifacts, such as metal streaks or limited-angle artifacts, if training targets expose them.
The recall and precision gains on 75–125 µm flaws suggest that PnP with 2.5D priors could lower missed-defect rates in nondestructive evaluation, but the false-positive increase under high noise and extreme sparsity implies production use would need a confidence or size filter.
A natural testable extension is to vary the input stack depth (3, 5, or 7 slices) and measure the trade-off between context and compute; the paper fixes it at five without an ablation.
If the synthetic-to-experimental transfer holds broadly, a shared artifact-reduction prior could be trained once on CAD-derived phantoms and deployed across many industrial XCT systems, avoiding per-scanner retraining.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Bottom line: it is a clean, modest A/B result. Swapping the 2D artifact-reduction CNN in the authors' own PnP framework for a 2.5D UNet improves reconstruction quality and defect detection on synthetic in-distribution data and one experimental Al-Ce part, at essentially no extra compute. The comparison is fair: both methods share the same beta grid search, CG steps, iteration count, and training recipe. The domain-transfer result—a prior trained entirely on simulated scans working on a real 145-view scan—is genuinely useful for nondestructive evaluation.

The paper is also honest. Section 7 admits the method struggles under OOD view sparsity, and Section 6 reports the precision trade-off at 73 views. That alone puts it ahead of a lot of reconstruction papers. Runtime and memory tables are there; 2.5D costs about two seconds and one extra gigabyte over 2D.

Soft spots, in proportion. The main one is evaluation against reconstructed references rather than known truth. The synthetic setup starts from CAD phantoms, so true ground-truth volumes exist, but the training target and evaluation reference is a dense 2132-view mono-energetic FDK reconstruction. That reference can still carry cone-beam artifacts. The cupping figure compares a line profile to that same FDK reference, which shows the network matches the reference, not necessarily that beam-hardening is truly gone from the object. Since the phantoms are known, a ground-truth comparison would settle this, and it should be trivial to run.

Second, there are no error bars or significance tests; every condition is one volume. Some differences are small, and in a couple of conditions 2D PnP wins on NRMSE or precision. The abstract's unqualified "improves the quality of reconstructions" overstates what is actually a conditional result that holds across most but not all tested regimes. The body is honest about this; the abstract is not.

Third, the experimental reference is itself an MBIR reconstruction, and the SNR/CNR numbers in Table 3 are absurdly high (CNR over 1300) because the PnP outputs are heavily smoothed. Those numbers do not mean the reconstruction is more faithful; they mean it is smoother. And the beam-hardening claim is never tested against a standard BH-correction baseline, so "eliminates the need for artifact correction pre-processing" is asserted, not demonstrated.

Who this is for: people doing PnP or learned priors for industrial XCT/NDE. They get a fair, reproducible-in-spirit comparison and a clear picture of where the 2.5D prior helps and where it does not. It does not reshape the field.

This deserves a serious referee. My own verdict would be major revision: add ground-truth evaluation on the synthetic phantoms, error bars or at least variance across slices, and a BH-correction baseline. With those, it would be a solid acceptance.

Referee Report

4 major / 3 minor

Summary. The paper proposes a plug-and-play (PnP) reconstruction method for sparse-view cone-beam XCT in which the proximal/regularization step is a 2.5D UNet that takes five adjacent slices and denoises/artifact-corrects the center slice. The method is compared with a 2D-prior PnP counterpart on synthetic aluminum AM phantoms (in-distribution and out-of-distribution noise/view counts) and on an experimental Al-Ce part scanned with 145 views, using a 580-view MBIR reconstruction as reference. The authors report improved NRMSE/SSIM and defect recall/precision for 2.5D PnP in most conditions, plus suppression of beam-hardening cupping, at roughly equal runtime and memory to 2D PnP, and much lower cost than MBIR.

Significance. If the reported gains hold against true object ground truth, the paper makes a modest but useful contribution: it validates a low-cost architectural change to a practical PnP framework, demonstrates that a synthetic-trained 2.5D prior transfers to experimental data, and shows that the extra computational burden over 2D PnP is negligible. The fixed Otsu-based defect-detection evaluation and the explicit runtime/memory comparison are strengths. The central limitation is that all quantitative comparisons are made against reconstructed references rather than known object truth; because the synthetic phantoms are CAD-generated, this is addressable and should be addressed before publication.

major comments (4)

[§3.3, Table 1; §4.1; Figs. 6, 9, 12] The synthetic evaluation uses a dense 2132-view mono-energetic FDK reconstruction as both the training target and the evaluation reference (Table 1). Since the CAD phantoms are known, true ground-truth volumes exist and should be used for NRMSE/SSIM and for recall/precision with known pore labels. As written, the reported gains of 2.5D PnP over 2D PnP may partly reflect better matching of the particular FDK reference's residual artifacts (cone-beam or cupping profile) rather than higher fidelity to the true object. The Conclusion's statement that pores "more closely match the ground truth" is therefore stronger than the evidence supports.
[§4, Table 2] All metrics in Table 2 are computed from a single reconstructed volume per condition; no noise realizations, bootstrap intervals, or significance tests are reported. The text in §4.1 says 2.5D PnP "consistently achieves significantly higher recall and precision," but the OOD-view rows contradict this (e.g., 73 views, noise 0.5: recall 0.879 for 2D PnP vs 0.306 for 2.5D PnP; precision 0.658 vs 0.306). The claims need to be qualified to the conditions where they hold, and error bars or repeated trials are needed before calling the differences significant.
[§5, Table 3] For the experimental demonstration, the reference is an MBIR reconstruction of a 580-view scan; all experimental image-quality and defect-detection metrics are relative to that reconstruction, which carries its own regularization bias. Moreover, Table 3 shows 2D PnP slightly outperforms 2.5D PnP on NRMSE and SSIM (0.148 vs 0.152; 0.991 vs 0.990), so the experimental advantage of 2.5D PnP rests entirely on recall/precision computed against an Otsu segmentation of the MBIR reference. The manuscript should acknowledge this reference-dependence more explicitly and ideally validate the experimental pipeline on a phantom with known defect locations.
[Abstract; §4.1, Fig. 4] The abstract claims that the 2.5D prior "eliminates the need for artifact correction pre-processing." The only evidence is the line profile in Fig. 4 compared with a mono-energetic dense FDK reference. No quantitative beam-hardening metric (e.g., cupping index) is provided, and no comparison against a standard BH-correction preprocessing pipeline is shown. The claim should either be supported by such a comparison or narrowed to "suppresses beam-hardening-like cupping relative to this reference."

minor comments (3)

[§3.1 and Algorithm 1] Eq. (6) defines the network as predicting a residual (input minus target), but Algorithm 1 writes z_k ← D_θ(x_{k-1}) as if D_θ outputs the denoised center slice directly. Please clarify whether D_θ outputs the residual or the cleaned slice, and make Algorithm 1 consistent with Eq. (6).
[Figure 1 caption] The caption calls the reference a "dense-view FDK reconstruction that does not contain beam hardening artifacts"; this is accurate for the synthetic setup, but the term "reference" should not be equated with ground truth elsewhere in the text (e.g., §4.1's wording about matching the reference).
[Table 2] Please report the number of defects/flaws in the reference segmentation used for recall and precision, and state how many voxels or pores contribute to the reported values; without this, the precision values for large pores are difficult to interpret.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 2.5D-vs-2D comparison is an empirical architecture study with independent external references.

full rationale

The central claim is an empirical comparison of two artifact-reduction priors inside the same plug-and-play framework, not a derivation from fitted constants. The training loss in Eq. (6) maps sparse-view FDK inputs to dense-view FDK references, and the same reference distribution is used for evaluation; this is standard supervised learning rather than circular reasoning, because the 2D and 2.5D priors are trained and evaluated under identical protocols on held-out scans. The paper inherits the PnP formulation, beta-selection rule, and hyperparameters from the authors' prior work [23], but that self-citation is not load-bearing for the novel claim: both compared methods share those components, so the reported 2.5D advantage is not forced by the inherited machinery. The beam-hardening suppression behavior is by construction of the paired training data (BH present in input, absent in reference), but reporting it as an empirical result is not a circular derivation. Concerns that dense-FDK or MBIR references are not true ground truth are validity limitations, not circularity, and the paper's own acknowledgment that it struggles on OOD view sparsity further indicates the results are not tautological.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The method introduces no new physical entities or conserved quantities. Its novelty is architectural. The main assumptions are standard XCT modeling choices plus the suitability of dense-view FDK and MBIR reconstructions as evaluation references. The only data-dependent tuning is the beta grid search, which is shared across methods.

free parameters (1)

Regularization parameter beta candidates = {2^{1-i}} for i=0,...,14
Selected per iteration via grid search on the reconstruction quality of a few center slices (inherited from [23]). This is data-dependent tuning that influences the final reconstruction, though it is applied identically to both 2D and 2.5D PnP.

assumptions (5)

domain assumption Cone-beam X-ray projection is modeled by a linear operator A, so the forward model y = Ax holds.
Standard model in XCT reconstruction, used in Section 2 and in the simulation pipeline.
domain assumption Photon noise is approximately Gaussian with variance proportional to signal intensity (Eq. 7).
Used to generate all synthetic training and test data; if this approximation is poor, the learned prior is trained on unrealistic noise.
domain assumption A dense-view (2132-view), mono-energetic FDK reconstruction is a sufficient training target for artifact and noise reduction.
The CNN is trained to map sparse, noisy, beam-hardened FDK to this reference. If the reference contains FDK artifacts, the prior learns to reproduce them.
domain assumption The PnP iteration converges or behaves well with the trained CNN prior, even though the network does not satisfy the standard nonexpansiveness or averaged-operator conditions.
The paper cites PnP convergence theory in Section 2 but does not verify these conditions for the trained UNet; in practice the method uses only 3 iterations with adaptive beta.
ad hoc to paper Five adjacent slices provide sufficient inter-slice context for artifact reduction; more slices or full 3D context would not meaningfully change the result.
The paper selects 5 slices based on prior 2.5D CT work, but does not ablate the number of slices or compare with a 3D prior.

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Cite this review

Pith. "Pith review of Plug-and-Play with 2.5D Artifact Reduction Prior for Fast and Accurate Industrial Computed Tomography Reconstruction." pith.science (2026). https://pith.science/paper/CA2DBR2T

@misc{pith2026250614719,
  author       = {Pith},
  title        = {Pith review of: Plug-and-Play with 2.5D Artifact Reduction Prior for Fast and Accurate Industrial Computed Tomography Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CA2DBR2T}},
  note         = {Machine review of arXiv:2506.14719}
}

read the original abstract

Cone-beam X-ray computed tomography (XCT) is an essential imaging technique for generating 3D reconstructions of internal structures, with applications ranging from medical to industrial imaging. Producing high-quality reconstructions typically requires many X-ray measurements; this process can be slow and expensive, especially for dense materials. Recent work incorporating artifact reduction priors within a plug-and-play (PnP) reconstruction framework has shown promising results in improving image quality from sparse-view XCT scans while enhancing the generalizability of deep learning-based solutions. However, this method uses a 2D convolutional neural network (CNN) for artifact reduction, which captures only slice-independent information from the 3D reconstruction, limiting performance. In this paper, we propose a PnP reconstruction method that uses a 2.5D artifact reduction CNN as the prior. This approach leverages inter-slice information from adjacent slices, capturing richer spatial context while remaining computationally efficient. We show that this 2.5D prior not only improves the quality of reconstructions but also enables the model to directly suppress commonly occurring XCT artifacts (such as beam hardening), eliminating the need for artifact correction pre-processing. Experiments on both experimental and synthetic cone-beam XCT data demonstrate that the proposed method better preserves fine structural details, such as pore size and shape, leading to more accurate defect detection compared to 2D priors. In particular, we demonstrate strong performance on experimental XCT data using a 2.5D artifact reduction prior trained entirely on simulated scans, highlighting the proposed method's ability to generalize across domains.

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