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arxiv: 2606.31318 · v1 · pith:V5PKGIZWnew · submitted 2026-06-30 · 💻 cs.CV

Wavelet-Optimized Pseudo-3D Accelerated Diffusion Model for Truncated Computed Laminography

Genyuan Zhang , Junyao Wang , Chuandong Tan , Fenglin Liu , Yongning Zhou This is my paper

Pith reviewed 2026-07-01 06:02 UTC · model grok-4.3

classification 💻 cs.CV
keywords Computed LaminographyTruncation ArtifactsDiffusion ModelWavelet RegularizationPseudo-3D ReconstructionModel-Based Iterative ReconstructionNondestructive Testing
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The pith

CL-DM uses a pseudo-3D diffusion model with wavelet regularization to reconstruct truncated laminography data beyond the field of view while enforcing consistency via MBIR.

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

The paper presents a new reconstruction technique for computed laminography when projected data is truncated by limited field of view. It first divides the space into data-complete, data-incomplete, and data-free regions, then deliberately targets the data-incomplete region for recovery. The method runs a standard 2D diffusion model on individual slices, couples it to a 3D model-based iterative step that enforces exact data consistency with the measurements, and adds wavelet regularization along the slice direction plus translation-invariant and low-frequency strategies to keep neighboring slices continuous. A fast 3D sampling schedule speeds up the process. If correct, the approach would allow nondestructive testing of larger plate objects with fewer artifacts and more complete 3D volumes than current 2D deep-learning methods that stay inside the measured field of view.

Core claim

By extending the reconstruction target into the data-incomplete region and combining 2D diffusion slice aggregation with 3D MBIR for strict consistency plus wavelet regularization along z, the CL-DM method removes truncation artifacts and recovers high-fidelity continuous 3D structures in both simulated and real computed laminography experiments.

What carries the argument

The CL-DM architecture: a 2D diffusion model for slice-wise generation, tied to 3D MBIR for data consistency, with wavelet regularization in the z-direction, translation-invariant mechanism, and low-frequency preservation to maintain inter-slice continuity.

If this is right

  • Effective imaging range expands because reconstruction now covers the data-incomplete region instead of stopping at the FOV boundary.
  • Data consistency with measured projections remains strict because the 3D MBIR step is retained at each iteration.
  • Inter-slice continuity improves through wavelet regularization combined with translation-invariant and low-frequency preservation.
  • Inference time drops substantially due to the introduced 3D fast sampling architecture.
  • Truncation artifacts are reduced and high-fidelity continuous 3D structures are restored, as shown in both simulations and real experiments.

Where Pith is reading between the lines

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

  • The same pseudo-3D pattern of 2D diffusion plus 3D consistency enforcement could be tested on other truncated tomography modalities such as limited-angle CT.
  • Shorter scan times for large flat objects become feasible if the method reliably recovers the missing region without extra projections.
  • Industrial nondestructive testing workflows could shift from 2D slice-by-slice networks to this hybrid diffusion-MBIR form if the continuity guarantees hold across varied truncation geometries.
  • Further experiments that deliberately vary the size of the data-incomplete region would reveal the practical limits of the wavelet-regularization step.

Load-bearing premise

Extending reconstruction into the data-incomplete region plus wavelet regularization will keep data consistency and slice continuity without creating new artifacts that the MBIR step cannot correct.

What would settle it

Reconstructed volumes in the data-incomplete region that violate the original projection measurements or show visible slice-to-slice discontinuities after the full pipeline would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.31318 by Chuandong Tan, Fenglin Liu, Genyuan Zhang, Junyao Wang, Yongning Zhou.

Figure 1
Figure 1. Figure 1: Overview of the proposed CL-DM framework. (a) Slices are generated using a standard 2D diffusion model. An Alternating Direction Method of Multipliers (ADMM) is subsequently employed to enforce data consistency, incorporating a 𝑧-directional wavelet regularization prior. (b) Schematic diagram of the Computed Laminography (CL) scanning geometry. (c) Illustration of the 3D accelerated sampling strategy, whic… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic diagram of sampling region division in truncated scanning mode. (a) RCL scanning mode; (b) Sampling region division. 𝑑 is the detector pixel width, and 𝜑 is the CL scanning tilt angle. Assuming the reconstructed voxel matrix dimensions of the scanned object are 𝑙 × 𝑤 × ℎ (with ℎ in the thickness direction) and the voxel size is 𝑑 ′ , its maximum physical cross-sectional radius is defined as 𝑅𝑚𝑎𝑥 … view at source ↗
Figure 3
Figure 3. Figure 3: a: The comparison of different regularization meth￾ods, from left to right, is ground truth, TV regularization in the z-direction, wavelet regularization in the z-direction, and wavelet regularization in the z-direction with TI. b: A schematic diagram of the TI mechanism and the low-frequency protection strategy. the shift = 0, we extract coefficients 𝑐0 = Ψ𝑧 (𝐱) from the for￾ward wavelet transform, and th… view at source ↗
Figure 4
Figure 4. Figure 4: real world CL imaging: (a) CL system; (b) Scanned object 4.1.1. Simulation Datasets In the creation of the simulation experiment dataset, for each batch of samples, they were destructively cut into small pieces that fit the field of view. High-fidelity images were then reconstructed using the CL-FBP algorithm to obtain the baseline ground truth, and two types of dedicated datasets were constructed based on… view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative results of non-global truncated data. From top to bottom: 3D rendering results, in-plane results, difference map, and layered results. The window for the in-plane results is [0,1], and the window for the layered results is [0.1,0.7]. The PSNR and SSIM indices are shown in the lower right corner of the in-plane map. From left to right: ground truth, FBP algorithm reconstruction results, and vari… view at source ↗
Figure 6
Figure 6. Figure 6: Qualitative results of global truncated data. In GT, the area outside the yellow dashed circle is the unsampled area, the area inside the orange circle is the data complete area, and the area between two circles is the incomplete data area. For the results of all methods, we only retained the area inside the circle. From top to bottom: three in-plane results and layered results. The window for the in-plane… view at source ↗
Figure 7
Figure 7. Figure 7: Qualitative results of real-world non-global truncated data. From top to bottom: 3D rendering results, two in-plane results, enlarged image (green and red boxes), and layered results. The window for the in-plane and layered results are [0,1]. From left to right: FBP algorithm reconstruction results, and various comparative algorithms; the last column shows the proposed algorithm [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 8
Figure 8. Figure 8: Qualitative results of real-world global truncated data. From top to bottom: Results from three horizontal planes and layered results. The window for the in-plane and layered results are [0,1]. From left to right: FBP algorithm reconstruction results, and various comparative algorithms; the last column shows the proposed algorithm [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Gray-scale distribution of different methods on the yellow line. (a) Non-global truncation, (b) Global truncation. that the z-directional regularization is significantly superior to multi-directional regularization. 5.2. Discussion on Advantages and Disadvantages of Our Method Experimental results show that the proposed method outperforms other competing models both quantitatively and qualitatively, and ex… view at source ↗
Figure 10
Figure 10. Figure 10: Visual evaluation results of the ablation study. The second row shows the difference maps with a window of [-0.2, 0.2] [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Visual evaluation results of regularization with different directions. The second and fourth rows are difference maps with a window of [-0.2, 0.2]. z- and xyz- denote regularization in the z-direction and xyz three directions, respectively. with end-to-end learning. 2) We elegantly solve the 3D CL truncation problem using a method that combines 2D priors with z-directional regularization, achieving superi… view at source ↗
read the original abstract

Computed Laminography (CL) is a key technology for the nondestructive testing of large plate-shaped objects. However, field-of-view (FOV) limitations inevitably lead to truncation of projected data, an ill-posed inverse problem that causes severe reconstruction artifacts. Existing deep learning methods typically rely on 2D architectures that lack rigorous data consistency constraints. Furthermore, they conventionally confine artifact removal strictly to the FOV, discarding potentially recoverable information outside it. To overcome these limitations, we first introduce a comprehensive CL FOV analysis, categorizing the space into data-complete, data-incomplete, and data-free regions. By extending our reconstruction target to encompass the data-incomplete region, we significantly expand the effective imaging range and enhance scanning efficiency. To achieve this, we propose a novel wavelet-optimized pseudo-3D accelerated diffusion model for CL truncation reconstruction (CL-DM). Our method utilizes a standard 2D diffusion model for slice aggregation, combined with a 3D model-based iterative reconstruction (MBIR) method to ensure strict data consistency. To mitigate inter-slice discontinuities, we introduce wavelet regularization along the z-direction, paired with a translation-invariant (TI) mechanism and a low-frequency preservation strategy. Finally, we introduce a 3D fast sampling architecture, significantly accelerating inference speed. Extensive simulations and real-world experiments demonstrate that CL-DM is superior in effectively eliminating truncation artifacts and restoring high-fidelity, continuous 3D structures.

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 / 1 minor

Summary. The manuscript proposes CL-DM, a wavelet-optimized pseudo-3D accelerated diffusion model for truncated computed laminography reconstruction. It first provides a FOV analysis dividing space into data-complete, data-incomplete, and data-free regions, then extends reconstruction into the data-incomplete region. The method uses a standard 2D diffusion model for slice aggregation, integrates 3D MBIR to enforce data consistency, applies wavelet regularization along z with a translation-invariant mechanism and low-frequency preservation to ensure inter-slice continuity, and introduces a 3D fast sampling architecture for acceleration. Extensive simulations and real experiments are stated to demonstrate superiority in artifact elimination and restoration of high-fidelity continuous 3D structures.

Significance. If the data-consistency integration and performance claims are substantiated, the work could meaningfully advance nondestructive testing of large plate-like objects by expanding the effective imaging range beyond conventional FOV limits and accelerating inference, with the pseudo-3D diffusion-plus-MBIR-plus-wavelet combination offering a practical route for ill-posed tomographic problems.

major comments (2)
  1. [Abstract] Abstract: the assertion that 'extensive simulations and real-world experiments demonstrate that CL-DM is superior' is unsupported by any quantitative metrics (PSNR, SSIM, etc.), baseline comparisons, error bars, or details on data exclusion/hyperparameter selection, which directly undermines verification of the central superiority claim.
  2. [Method integration] Method integration (described in the abstract and likely §3): the claim that 3D MBIR enforces strict data consistency after 2D diffusion outputs and z-direction wavelet regularization lacks explicit equations, pseudocode, or algorithmic steps showing how consistency violations in the data-incomplete region are detected and corrected; this is load-bearing for the data-fidelity guarantee.
minor comments (1)
  1. [Introduction] The FOV categorization into data-complete/incomplete/free regions is clearly motivated and could be highlighted earlier as a standalone contribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and outline the planned revisions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that 'extensive simulations and real-world experiments demonstrate that CL-DM is superior' is unsupported by any quantitative metrics (PSNR, SSIM, etc.), baseline comparisons, error bars, or details on data exclusion/hyperparameter selection, which directly undermines verification of the central superiority claim.

    Authors: We agree that the abstract would be strengthened by including key quantitative results. The manuscript body reports PSNR/SSIM comparisons, baseline methods, error bars, and experimental protocols, but these are not summarized in the abstract. We will revise the abstract to incorporate representative metrics (e.g., average PSNR gains over baselines) and a brief note on the evaluation protocol. This directly addresses the verifiability concern. revision: yes

  2. Referee: [Method integration] Method integration (described in the abstract and likely §3): the claim that 3D MBIR enforces strict data consistency after 2D diffusion outputs and z-direction wavelet regularization lacks explicit equations, pseudocode, or algorithmic steps showing how consistency violations in the data-incomplete region are detected and corrected; this is load-bearing for the data-fidelity guarantee.

    Authors: We acknowledge that the current description of the MBIR integration step would benefit from greater explicitness. Section 3 outlines the combination of 2D diffusion outputs with 3D MBIR and wavelet regularization, but additional equations and pseudocode would clarify detection and correction of consistency violations in the data-incomplete region. We will add a dedicated algorithmic box with pseudocode and the relevant data-consistency projection equations. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical architecture with external validation

full rationale

The paper describes CL-DM as an empirical pipeline (2D diffusion for slice aggregation + 3D MBIR for data consistency + wavelet regularization along z with TI and low-frequency preservation + fast sampling). No equations, parameters, or claims are shown to reduce by construction to fitted inputs, self-citations, or renamed known results. The central claims rest on simulation and real-world experiments evaluated against external benchmarks, satisfying the self-contained criterion.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No explicit free parameters, axioms, or invented entities are stated in the abstract; the approach relies on standard diffusion models and MBIR as background techniques.

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discussion (0)

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    Appendix 7.1. Detailed Derivation of Sampling Region Boundaries To analyze the sampling characteristics in truncated scanning, a geometric equivalent transformation is em- ployed, where the object remains stationary while the X- ray source and detector perform a relative circular motion around it[cite: 26]. The geometric center of the PCB is G. Zhang et a...