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arxiv: 2510.06516 · v2 · submitted 2025-10-07 · 💻 cs.CV

Limited-Angle Tomography Reconstruction via Projector Guided 3D Diffusion

Zhantao Deng , M\'eriem Er-Rafik , Anna Sushko , C\'ecile H\'ebert , Pascal Fua This is my paper

Pith reviewed 2026-05-18 08:37 UTC · model grok-4.3

classification 💻 cs.CV
keywords limited-angle tomographyelectron tomography3D diffusion modelsmissing wedgeTEM reconstructionFIB-SEM simulationprojector guidanceiterative reconstruction
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The pith

A 3D diffusion model trained only on simulated TEM data from FIB-SEM volumes reconstructs accurate structures from real limited-angle electron tomography projections without retraining.

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

The paper introduces TEMDiff, a diffusion-based method that learns 3D structural priors by simulating TEM tilt series from readily available FIB-SEM volumes. This sidesteps the need for hard-to-obtain clean 3D ground truth from actual electron microscopes. Operating directly on volumetric data lets the model enforce consistency across slices implicitly. On simulated limited-angle cases the approach yields higher-quality reconstructions than prior methods, and the same trained model transfers directly to real TEM acquisitions, recovering usable structures even when the tilt range is restricted to just 8 degrees.

Core claim

TEMDiff is a projector-guided 3D diffusion framework trained on FIB-SEM volumes converted to TEM tilt series by a simulator; once trained it performs iterative reconstruction on new limited-angle projections, implicitly enforcing 3D consistency and generalizing to real TEM data acquired under different conditions without any fine-tuning.

What carries the argument

Projector-guided 3D diffusion model that iteratively refines a 3D volume while using the forward projector to enforce consistency with the observed 2D tilt projections.

If this is right

  • Reconstruction quality on simulated limited-angle datasets exceeds current state-of-the-art methods.
  • A single trained model recovers accurate structures from real TEM tilt series spanning only 8 degrees at 2-degree increments.
  • No additional regularization is required because 3D operation already enforces slice-to-slice consistency.
  • Training relies solely on FIB-SEM volumes and a simulator, removing the need for paired clean 3D TEM ground truth.

Where Pith is reading between the lines

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

  • The same simulator-driven training strategy could be adapted to other tomography modalities that suffer from missing data angles.
  • If the simulator fidelity proves robust across sample types, the method could lower the experimental cost of collecting wide-angle tilt series in routine electron microscopy work.
  • Narrow-angle reconstructions might enable faster in-situ experiments where mechanical tilt limits or sample stability constrain the angular range.

Load-bearing premise

The simulator that converts FIB-SEM volumes into synthetic TEM tilt series produces data whose structural statistics match real TEM acquisitions closely enough for the learned priors to transfer without retraining.

What would settle it

Apply the trained model to a real TEM tilt series whose true 3D structure is independently known from a wider tilt range or orthogonal imaging; if the narrow-angle reconstruction deviates substantially in shape or density from that reference, the generalization claim fails.

Figures

Figures reproduced from arXiv: 2510.06516 by Anna Sushko, C\'ecile H\'ebert, M\'eriem Er-Rafik, Pascal Fua, Zhantao Deng.

Figure 1
Figure 1. Figure 1: Mitochondria reconstructed using FBP, SART, DiffusionMBIR, DOLCE, and TEMDiff, with tilts covering 10◦ with 1 ◦ increments. The top row presents 3D views, while the bottom row displays vertical cross￾section along x axis of each corresponding 3D view. TEMDiff produces more clear, more consistent and better structures than others in both views. The contrast for these other methods has been enhanced for bett… view at source ↗
Figure 2
Figure 2. Figure 2: The TEMDiff pipeline. (Top) At inference time, given the acquired tilts y, the inverse radon transform C = R−1(y) is computed and concatenated with noise. The result is fed to the pretrained U-Net N which includes attention layers and takes the acquisition angular range θ and increments ∆θ as further inputs. The U-Net N estimates the amount of noise in the input and iteratively denoise it. (Bottom) To trai… view at source ↗
Figure 3
Figure 3. Figure 3: Reconstructions of FBP, SART and TEMDiff with real tilts of 8 ◦ angular range and 1 ◦ or 2 ◦ increments. The reference volumes are reconstructed using AreTomo with all available tilts (80◦ or 120◦). Each main figure is the 3D view of reconstruction and its bottom-right inset corresponds to one slice of 2D view. TEMDiff produces more realistic and clearer reconstructions with good contrast on both 3D and 2D… view at source ↗
Figure 5
Figure 5. Figure 5: During training, tilt angle θ and increments ∆θ are randomly sampled from predefined ranges and (12) is applied to generate STEM tilt series used for training. IV. RESULTS The entire TEMDiff pipeline is applied to raw tilt series of biological samples with different thicknesses (≈300nm, 500nm, 1000nm), acquired over ranges of 8 ◦ with 1 ◦ or 2 ◦ increments using either TEM or STEM [PITH_FULL_IMAGE:figures… view at source ↗
Figure 6
Figure 6. Figure 6: Example of reconstruction before and after histogram adjust￾ment. (a) ground truth (b) reconstruction from Aretomo before adjust￾ment with high RMSE and (c) reconstruction after adjustment with lower RMSE. ground truth and reconstructed volumes is applied before metric calculation. C. Results 1) Simulated Datasets from FIB-SEM: Each method is trained and evaluated on simulated FIB-SEM datasets with angular… view at source ↗
Figure 5
Figure 5. Figure 5: Histogram (left) and examples (right) of (a) real STEM tilts, (b) simulated STEM tilts with proposed mapping, and (c) radon transform of FIB-SEM volume. The tilts synthesized by the proposed mapping are visually and statistically close to real STEM tilts. are provided in the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Typical vertical cross-section along x axis of 3D volumes reconstructed from different methods on real-tilts-simulated data. The reference is reconstructed via Aretomo with 80◦ or 120◦ angular range. In both 10◦ and 60◦ cases, TEMDiff produces more plausible reconstructions with streaking reduced and yields good cross-slice consistency. Visual inspection (Figs. 8-11) further confirms that TEMDiff produces … view at source ↗
Figure 8
Figure 8. Figure 8: Three mitochondria reconstructed by different methods from simulated projections with an angular range of 10◦. Reference reconstructions are obtained via Aretomo with tilting series covering 120◦ (top row) and 80◦ (the second and third row). Green represents ground truth volume and red represent error volume, i.e. red means the presence of the difference between ground truth and reconstructed volumes. In e… view at source ↗
Figure 9
Figure 9. Figure 9: Three mitochondria reconstructed by different methods from simulated projections with angle range of 60◦. Reference reconstructions are obtained via Aretomo with tilting series covering 120◦ (top row) and others with 80◦. Green represents ground truth volume and red represent error volume, i.e. red means the presence of the difference between ground truth and reconstructed volumes. In each bottom-right ins… view at source ↗
Figure 10
Figure 10. Figure 10: Three synapses reconstructed by different methods from simulated projections with angle range of 10◦. Reference reconstructions are obtained via Aretomo with tilting series covering 120◦ (top row) and others with 80◦. Green represents ground truth volume and red represent error volume, i.e. red means the presence of the difference between ground truth and reconstructed volumes. In each bottom-right inset,… view at source ↗
Figure 11
Figure 11. Figure 11: Three synapses reconstructed by different methods from simulated projections with angle range of 60◦. Reference reconstructions are obtained via Aretomo with tilting series covering 120◦ (top row) and others with 80◦. Green represents ground truth volume and red represent error volume, i.e. red means the presence of the difference between ground truth and reconstructed volumes. In each bottom-right inset,… view at source ↗
read the original abstract

Limited-angle electron tomography aims to reconstruct 3D shapes from 2D projections of Transmission Electron Microscopy (TEM) within a restricted range and number of tilting angles, but it suffers from the missing-wedge problem that causes severe reconstruction artifacts. Deep learning approaches have shown promising results in alleviating these artifacts, yet they typically require large high-quality training datasets with known 3D ground truth which are difficult to obtain in electron microscopy. To address these challenges, we propose TEMDiff, a novel 3D diffusion-based iterative reconstruction framework. Our method is trained on readily available volumetric FIB-SEM data using a simulator that maps them to TEM tilt series, enabling the model to learn realistic structural priors without requiring clean TEM ground truth. By operating directly on 3D volumes, TEMDiff implicitly enforces consistency across slices without the need for additional regularization. On simulated electron tomography datasets with limited angular coverage, TEMDiff outperforms state-of-the-art methods in reconstruction quality. We further demonstrate that a trained TEMDiff model generalizes well to real-world TEM tilts obtained under different conditions and can recover accurate structures from tilt ranges as narrow as 8 degrees, with 2-degree increments, without any retraining or fine-tuning.

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 / 2 minor

Summary. The manuscript introduces TEMDiff, a 3D diffusion-based iterative reconstruction framework for limited-angle electron tomography. It is trained on FIB-SEM volumetric data mapped to TEM tilt series via a simulator to learn structural priors without requiring real TEM ground truth. The method operates directly on 3D volumes for implicit slice consistency and claims to outperform state-of-the-art methods on simulated limited-angle datasets while generalizing zero-shot to real TEM acquisitions, recovering accurate structures from tilt ranges as narrow as 8° (2° increments) without retraining or fine-tuning.

Significance. If the generalization results hold under rigorous domain-shift validation, the work would be significant for electron microscopy by enabling high-quality limited-angle reconstructions using abundant FIB-SEM data and simulation rather than scarce paired TEM ground truth. The projector-guided 3D diffusion approach, which enforces volumetric consistency without additional regularization, represents a technically interesting direction for tomography priors.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Results on real-world TEM tilts): The central claim of zero-shot generalization to real TEM data acquired under different conditions (including 8° tilt ranges) rests on the unquantified assumption that the FIB-SEM-to-TEM simulator reproduces the relevant marginal statistics (contrast, noise, multiple scattering). No feature-space distances, ablation on domain randomization, or cross-domain error metrics are reported to substantiate this alignment, which directly undermines the no-retraining transfer result.
  2. [§3] §3 (Method, projector guidance): The description of how the projector is integrated into the 3D diffusion sampling process lacks sufficient implementation detail (e.g., exact form of the guidance term, weighting schedule, or handling of the missing wedge during iterative reconstruction) to support reproducibility or to verify that the claimed consistency enforcement is achieved without additional regularization.
minor comments (2)
  1. [Abstract] The abstract states outperformance and generalization but provides no numerical metrics, ablation summaries, or table references; adding a brief quantitative highlight would improve readability.
  2. [§2 and §3] Notation for the diffusion process and projector operator should be introduced consistently in §2 before use in §3 to avoid ambiguity for readers unfamiliar with conditional diffusion models.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. We address each major point below and indicate the revisions we will incorporate to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Results on real-world TEM tilts): The central claim of zero-shot generalization to real TEM data acquired under different conditions (including 8° tilt ranges) rests on the unquantified assumption that the FIB-SEM-to-TEM simulator reproduces the relevant marginal statistics (contrast, noise, multiple scattering). No feature-space distances, ablation on domain randomization, or cross-domain error metrics are reported to substantiate this alignment, which directly undermines the no-retraining transfer result.

    Authors: We acknowledge that additional quantitative validation of the simulator's fidelity would strengthen the zero-shot generalization claim. The current results rely on visual and quantitative reconstruction quality on real TEM data at narrow tilt ranges, which would be infeasible without sufficient distributional alignment. In the revised manuscript we will add feature-space metrics (e.g., FID scores computed on simulated versus real tilt-series projections) together with a brief ablation on key domain-randomization parameters to provide explicit evidence of marginal-statistic alignment. revision: yes

  2. Referee: [§3] §3 (Method, projector guidance): The description of how the projector is integrated into the 3D diffusion sampling process lacks sufficient implementation detail (e.g., exact form of the guidance term, weighting schedule, or handling of the missing wedge during iterative reconstruction) to support reproducibility or to verify that the claimed consistency enforcement is achieved without additional regularization.

    Authors: We agree that greater implementation detail is needed for reproducibility. In the revised Section 3 we will supply the exact mathematical expression for the projector-guidance term, the schedule used to modulate its weight across diffusion timesteps, and a clear description of how the missing-wedge region is masked during the consistency-enforcement step. We will also include pseudocode for the full sampling loop to make the integration explicit. revision: yes

Circularity Check

0 steps flagged

No circularity; training and evaluation use external FIB-SEM data plus simulator

full rationale

The paper trains TEMDiff on volumetric FIB-SEM data converted to limited-angle TEM tilt series by an external simulator, then reports reconstruction performance on both simulated test sets and real TEM acquisitions without retraining. No equations, loss terms, or performance metrics in the abstract or described method reduce a claimed output to a quantity defined by the model's own fitted parameters or by a self-citation chain. The zero-shot transfer claim rests on an unverified domain-similarity assumption rather than any definitional or fitting loop internal to the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the unverified transferability of priors learned from a FIB-SEM-to-TEM simulator and on the implicit assumption that 3D diffusion models can enforce slice consistency without explicit regularization terms.

axioms (1)
  • domain assumption The simulator accurately reproduces the noise and contrast statistics of real TEM tilt series from FIB-SEM volumes.
    Invoked to justify training without real TEM ground truth.

pith-pipeline@v0.9.0 · 5764 in / 1249 out tokens · 26488 ms · 2026-05-18T08:37:40.092757+00:00 · methodology

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