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Advanced Brain Tissue Imaging with Data-Consistent Diffusion Priors in Laminographic X-Ray Nanoimaging
Wenxuan Fang, Abraham L. Levitan, Ana Diaz, Carles Bosch, Adrian Wanner, Andreas T. Schaefer, Mirko Holler, Tomas Aidukas, Nicholas W. Phillips, Yuxin Zhang, Alexandra Pacureanu, Manuel Guizar-Sicairos, Luis Barba
TL;DR
Laminography’s missing-cone geometry makes faithful 3D brain reconstruction difficult, while direct 3D learning is limited by scarce data and computational cost. LUCID combines multi-view diffusion priors with physics-based data consistency, restoring missing Fourier information and producing high-fidelity reconstructions across simulated and experimental data. The approach supports reliable recovery of fine neural structures while reducing dependence on fully sampled 3D training data.
Problem
Laminography leaves a 3D missing cone, while direct 3D learning is constrained by scarce volumetric data and high computational cost.
Method
LUCID embeds sequential axial, sagittal, and coronal diffusion priors within iterative laminography data-consistency updates, using tomography reconstructions for training.
Results
LUCID restores missing Fourier information and yields high-fidelity reconstructions with enhanced isotropy and structural continuity on simulated and real laminography data.
Takeaways & Limitations
LUCID provides a data-consistent route to recovering fine neural features and coherent microarchitecture for connectomic and tissue-level analysis.
Takeaways & Limitations
The approach addresses computational cost through multi-view 2D inference, but its training and evaluation span tomography-derived volumes and laminography data with a modality domain gap.
Abstract
from arXiv · showhide
Nanoscale imaging of mammalian brains is critical for connectomics. X-ray laminography enables high-throughput imaging of extended, plate-like biological specimens. However, the tilted acquisition geometry leads to incomplete Fourier-space coverage, giving rise to a missing-cone of information. Conventional reconstruction methods cannot recover unmeasured information within the cone, resulting in artifacts that distort fine brain structures. While resolving these requires modeling 3D structure, direct 3D deep learning approaches are limited by data scarcity and computational cost. Here we introduce LUCID (Laminography with Unified Consistent Diffusion), a framework that combines multi-view diffusion priors with projection-domain data consistency. LUCID integrates complementary 3D structural information while enforcing strict alignment with the laminography forward model. On simulated datasets, LUCID substantially improves spatial fidelity and restores missing Fourier components, outperforming baseline methods. Applied to experimental laminography data, LUCID generalizes robustly despite being trained exclusively on fully sampled tomographic volumes, and effectively recovers unmeasured Fourier information.
1 Introduction
Laminography offers a promising route to high-throughput nanoscale brain imaging, but its tilted geometry leaves a missing cone that makes reconstruction intrinsically 3D and difficult. LUCID addresses this gap by combining multi-view diffusion priors with iterative projection-domain data consistency, supporting evaluation on simulated and experimental data.
- Motivation: Nanoscale connectomics requires resolving synaptic features at approximately 10–20 nm across millimeter-scale tissue volumes.This scale remains difficult to achieve with three-dimensional imaging methods.
- Motivation: Laminography suits extended brain sections because tilted X-ray imaging penetrates thicker tissue and avoids cylindrical sample preparation.Its geometry provides more balanced Fourier sampling than limited-angle tomography, although information remains missing.
- The missing-cone problem: The tilted rotation geometry leaves a biconical region of 3D frequency space unsampled, producing anisotropic information loss and reconstruction artifacts.This missing-cone problem makes recovery intrinsically volumetric rather than separable into independent 2D slices.
- Existing limitations: Conventional FBP cannot compensate for missing-cone artifacts, while post-processing learning methods remain decoupled from measured projections and cannot genuinely recover missing information.Existing iterative approaches only partially mitigate the problem by estimating unmeasured information through data-error minimization.
- Existing limitations: Direct 3D learning is constrained by scarce volumetric data and prohibitive computational demands, while slice-wise 2D methods sacrifice volumetric consistency.Brain heterogeneity further complicates learning useful structural priors from methods developed largely for industrial materials.
- Proposed approach: LUCID embeds axial, sagittal, and coronal diffusion priors within an iterative laminography reconstruction loop that jointly updates generated structure and projection-domain consistency.The work evaluates the framework on simulated data and demonstrates cross-domain generalization to experimental laminography despite training on tomographic volumes.
2 Results
LUCID alternates multi-view diffusion denoising with laminography data consistency to reconstruct anatomically coherent, measurement-consistent volumes. Across simulated and experimental data, it improves spatial fidelity, uncertainty characterization, and recovery of missing-cone Fourier information.
- LUCID framework: LUCID iteratively alternates a multi-view diffusion prior with laminography data-consistency updates, refining noisy 3D volumes into measurement-consistent reconstructions.The diffusion module processes axial, sagittal, and coronal slices with dedicated 2D denoisers, while the consistency module compares forward projections with measured projections.
- LUCID framework: The diffusion prior is trained on high-resolution tomography volumes decomposed into axial, sagittal, and coronal slices, enabling efficient learning of volumetric anatomical structure.Each view uses a denoising diffusion model trained to reverse a fixed noising process.
- Simulated-data reconstruction: Compared with FBP and GD, LUCID recovers fine synaptic-like structures and plasma membranes with improved contrast, continuity, and boundary definition.These improvements are visible in localized regions of interest and approach the ground-truth appearance.
- Simulated-data reconstruction: More than 13 dB PSNR improvement and nearly 75% RMSE reduction versus FBP demonstrate higher spatial-domain reconstruction fidelity for LUCID.LUCID also provides consistent pixel-wise and perceptual gains over iterative GD.
- Uncertainty evaluation: Uncertainty is highest in missing-cone-affected, structurally ambiguous regions, while coherent ultrastructural patterns show lower uncertainty and can be distinguished for downstream analysis.The uncertainty map is computed from multiple stochastic reconstructions and can guide caution in connectome reconstruction and segmentation.
- Spectral evaluation: LUCID increases Fourier energy within the missing cone, achieving the highest cone spectral fidelity and recovered spectral energy while approaching the isotropic ground-truth distribution.The restored frequency content corresponds to improved recovery of high-frequency spatial information.
- Experimental-data reconstruction: Without retraining or fine-tuning, LUCID generalizes from simulated tomographic training data to experimental laminography, recovering line-like neural structures and more missing-cone spectral energy.Experimental reconstructions show reduced anisotropy, clearer tissue boundaries, and a more isotropic frequency distribution.
3 Discussion
LUCID combines multi-view diffusion priors with laminography data consistency to reconstruct brain tissue from incomplete measurements. The framework improves missing-cone recovery, supports data-efficient reconstruction, and is intended to enable reliable large-volume brain imaging.
- 3 Discussion: LUCID combines multi-view diffusion priors with laminography data consistency for physics-guided brain-volume reconstruction.It uses axial, sagittal, and coronal perspectives while enforcing the laminography forward model.
- 3 Discussion: LUCID restores missing-cone information with enhanced isotropy and structural continuity in simulated and experimental laminography data.The framework recovers fine neural features such as elongated axonal and dendritic structures.
- 3 Discussion: The released nanoscale brain laminography dataset is intended to support reconstruction-method development and common benchmarks.The authors describe it as the first released nanoscale brain laminography dataset.
- 3 Discussion: LUCID provides a data-efficient route to augment brain-imaging datasets when diverse training data are restricted by privacy or acquisition constraints.The authors connect this capability to technically and ethically challenging collection of large annotated 3D neuroscience datasets.
- 3 Discussion: The framework reduces the computational cost of volumetric generative modeling through efficient 2D inference while maintaining 3D coherence.Its multi-view strategy integrates axial, sagittal, and coronal perspectives.
- 3 Discussion: LUCID establishes a data-consistent foundation for large-volume brain reconstruction and other imaging problems with incomplete data.The authors frame this as bridging physical modeling and generative intelligence in X-ray nanoimaging.
4.1 Dataset and implementation details
The study evaluates LUCID using mouse-brain PXCT data, simulated laminography acquisitions, and image- and Fourier-domain metrics. The simulation uses an undersampled tilted geometry, while the implementation combines multi-view diffusion training with quantitative spectral-completeness assessment.
- Dataset and implementation details: The experimental benchmark uses high-resolution ptychographic X-ray tomography datasets of mouse brain tissue acquired at the cSAXS beamline.The preparation and imaging protocol were designed to preserve structure and provide synaptic-resolution contrast.
- Dataset and implementation details: The samples were prepared from 600 µm horizontal brain sections and resin-embedded through staged resin-acetonitrile processing and curing.The curing process used 80 °C, with the container lid opened to allow acetonitrile evaporation.
- Dataset and implementation details: Resin-embedded samples were trimmed into cylindrical pillars using diamond-knife preparation and a 30 keV Ga-ion beam before PXCT measurement.The pillars were mounted onto dedicated PXCT holders with Ga-assisted carbon deposition for mechanical stability.
- Dataset and implementation details: PXCT and laminographic measurements used coherent 6.2 keV X-rays with beamline-specific focusing optics.PXCT used the OMNY instrument, while mouse-brain PyXL measurements used the LamNI instrument at cSAXS.
- Dataset and implementation details: The dataset contains 10 mouse-brain tomograms with ultrastructural detail, voxel sizes from 38 nm to 81 nm, and varied volume dimensions.Training slices were sampled from the first nine tomograms across axial, sagittal, and coronal orientations.
- Dataset and implementation details: Simulations used a 61° tilt angle and 360 projections, compared with 723 projections predicted for Nyquist angular sampling.The resulting angular undersampling reproduces characteristic missing-cone sampling and Fourier-domain gaps.
- Dataset and implementation details: LUCID produced stable and structurally faithful reconstructions despite the undersampled acquisition regime.This result is attributed to diffusion-based priors compensating for incomplete angular sampling beyond classical reconstruction limits.
- Dataset and implementation details: Reconstruction fidelity was assessed with PSNR, SSIM, and RMSE over the full 3D brain volume.The evaluation also included Fourier-domain metrics for spectral completeness in the missing-cone region.
4.2 Inverse problem in X-ray laminography
Laminography reconstructs 3D objects from incomplete, geometry-dependent measurements, making the inverse problem ill-conditioned and producing directional artifacts that require learned priors with physical constraints.
- The reconstruction task is modeled as recovering an unknown 3D object x from X-ray projection measurements.
- Laminographic acquisition leaves a characteristic Fourier-domain deficit because its rotation axis is tilted relative to the beam.The incomplete sampling makes the laminographic operator A ill-conditioned.
- The ill-conditioned operator produces axial elongation, mixing between adjacent layers, and highly directional blurring artifacts.
- LUCID addresses these artifacts by combining a learned generative prior with explicit physical constraints.
4.3 Denoising diffusion probabilistic models
Denoising diffusion probabilistic models learn data distributions through forward noise addition and reverse denoising, and LUCID uses the reverse process as a prior for ill-posed laminography reconstruction.
- DDPMs learn complex data distributions through gradual forward noising and learned reverse denoising.
- The forward process is a Markov chain whose transitions add Gaussian noise to latent variables indexed by diffusion time.
- The noise magnitude at each step is controlled by a predefined variance schedule β_t.
- The reverse process is parameterized by a neural network s_θ that predicts the noise component at each diffusion step.
- During inference, sampling starts from x_T ∼ N(0, I) and applies reverse transitions, providing biologically and statistically coherent regularization for laminography reconstruction.
4.4 LUCID: Laminography with Unified Consistent Diffusion
LUCID combines orientation-specific diffusion priors with projection-domain data consistency in an iterative reconstruction loop, preserving complementary anatomical structure while enforcing agreement with measured laminography data.
- Multi-view diffusion prior: LUCID learns diffusion priors from axial, sagittal, and coronal views to capture complementary structural cues.
- Multi-view diffusion prior: At each diffusion step, view-specific denoisers update the noisy volume for axial, sagittal, or coronal orientations.
- Multi-view diffusion prior: The denoisers are followed by laminography data consistency, and the three views are cycled every three steps.
- Projection-domain data consistency: LUCID forms a noise-free clean-volume estimate from the current noisy state using Tweedie’s formula.
- Projection-domain data consistency: Measured projections are compared with forward-simulated projections, and gradient descent minimizes the projection-domain data-fidelity term.
- Projection-domain data consistency: The correction enforces physical measurement agreement while preserving diffusion-provided anatomical priors.
- Domain translation: A reversible domain translation maps real laminography reconstructions to a tomography-like intensity manifold and restores outputs afterward.
- Iterative reconstruction: The full process alternates diffusion priors, projection-domain consistency, and controlled noise reintroduction from t = T to t = 1.