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DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction
Jiaming Liu, Rushil Anirudh, Jayaraman J. Thiagarajan, Stewart He, K. Aditya Mohan, Ulugbek S. Kamilov, Hyojin Kim
TL;DR
Limited-angle CT is a severely ill-posed reconstruction problem, and prior methods often provide point estimates without uncertainty quantification. DOLCE uses a conditional diffusion prior with data-consistency updates; experiments report SOTA performance across different real-world image domains and uncertainty estimates consistent with reconstruction errors.
Problem
Limited-angle CT is severely ill-posed, and prior work often struggles to recover sharp details while producing only point estimates rather than uncertainty estimates.
Source: §1 · pp. 1–2Method
Results
Takeaways & Limitations
Abstract
from arXiv · showhide
Limited-Angle Computed Tomography (LACT) is a non-destructive evaluation technique used in a variety of applications ranging from security to medicine. The limited angle coverage in LACT is often a dominant source of severe artifacts in the reconstructed images, making it a challenging inverse problem. We present DOLCE, a new deep model-based framework for LACT that uses a conditional diffusion model as an image prior. Diffusion models are a recent class of deep generative models that are relatively easy to train due to their implementation as image denoisers. DOLCE can form high-quality images from severely under-sampled data by integrating data-consistency updates with the sampling updates of a diffusion model, which is conditioned on the transformed limited-angle data. We show through extensive experimentation on several challenging real LACT datasets that, the same pre-trained DOLCE model achieves the SOTA performance on drastically different types of images. Additionally, we show that, unlike standard LACT reconstruction methods, DOLCE naturally enables the quantification of the reconstruction uncertainty by generating multiple samples consistent with the measured data.
1. Introduction
Limited-angle coverage makes CT reconstruction severely ill-posed, challenging recovery of sharp edges and leaving uncertainty poorly characterized by point-estimate methods. DOLCE combines a conditional diffusion prior with data-consistency updates; experiments report strong results across distinct datasets and support uncertainty estimation.
1. Introduction
- Large missing-angle ranges remain challenging for sharp-edge reconstruction, while most prior methods produce only point estimates rather than quantifying uncertainty.Source: §1 · p. 2
- It conditions a repeated-refinement diffusion sampler on noisy seed reconstructions from transformed limited-angle sinograms and applies data consistency after each sampling update.Source: §1 · p. 2
- The same pre-trained DOLCE model achieves SOTA performance across human-body and checked-in-luggage images, including 512 × 512 reconstructions at limited angles of 60°, 90°, and 120°.Source: §1 · p. 2
- DOLCE generates diverse reconstructions whose estimated variances are reported as consistent with true reconstruction errors, enabling uncertainty quantification.Source: §1 · p. 2
- DOLCE is introduced as the first conditional diffusion model for recovering high-quality CT images from limited-angle sinograms.Source: §1 · p. 2
- DOLCE improves PSNR by at least 3 dB over ILVR [12] and DPS [13] across checked-in-luggage and medical-image datasets.Source: §1 · p. 2
- A 3D segmentation experiment demonstrates recovery of geometric structure and sharp edges even in severely ill-posed, high-resolution settings.Source: §1 · p. 2
2. Related Work
Prior CT reconstruction work includes analytic and iterative model-based methods, supervised deep networks, and denoising-driven approaches. Diffusion models enable stochastic image generation and have been adapted to inverse problems, but the cited work reports difficulties with severe LACT.
2. Related Work
- Filtered back projection can produce inaccurate, noisy, and artifact-prone reconstructions in ill-posed limited-angle or sparse-view settings; iterative methods instead combine measurement physics with an object prior.Source: §2 · p. 2
- Supervised deep-learning reconstructions can directly produce point estimates, while unfolded iterative algorithms integrate physical information through data-consistency blocks and trainable CNN regularizers.Source: §2 · p. 2
- Diffusion methods generate samples through sequential stochastic transitions and have been applied to conditional imaging tasks, including sparse-CT and MRI reconstruction.Source: §2 · p. 3
- For severely ill-posed LACT, current SOTA diffusion methods often fail to generate desired semantics and accurate details; DOLCE's overview alternates denoising and data-consistency updates.Source: §2 · p. 3, Figure 2 · p. 3
3. Preliminaries
Limited-angle CT reconstruction is an ill-posed linear inverse problem. The preliminaries describe diffusion models as adding noise to clean images and learning a reverse process that estimates them from noisy states.
Inverse Problems
- LACT reconstruction seeks an image x from incomplete measurements y = Ax, an ill-posed recovery that often requires assumptions about x.The posterior can be sampled, or summarized with MAP or MMSE point estimates.Source: §3 · p. 3
Denoising Diffusion Probabilistic Models
- DDPM adds Gaussian noise to clean images in a fixed forward process and learns neural-network transitions for the reverse process.The reverse chain runs from xT toward x0, estimating the clean image from a partially noisy state.Source: §3 · pp. 3–4
Improved Reverse Process
- The reverse transition uses a learned mean and variance; the network predicts noise, which is used to derive the transition mean.The paper adopts learned reverse variances and uses a neural network with separate output heads for the mean and variance.Source: §3 · pp. 3–4
4. Proposed Approach: DOLCE
DOLCE reconstructs full-view CT images by conditioning diffusion sampling on limited-angle sinogram data. Its iterative procedure combines denoising with data-consistency updates, using low-fidelity reconstructions as conditioning inputs.
4. Proposed Approach: DOLCE
- DOLCE conditions a diffusion model on a limited-angle sinogram-derived input to sample full-view CT images through T refinement steps.The paper presents this as the first use of conditional sampling for CT reconstruction.Source: §4 · p. 4
4.1. Optimizing the Conditional Denoising Network
- The denoising network uses a low-fidelity FBP or RLS reconstruction as its condition and can be trained with conditional and unconditional objectives.Randomly dropping the condition during training supports adjusted noise prediction at sampling; λ controls the trade-off, with λ > 1 strengthening conditional prediction.Source: §4.1 · p. 4
4.2. Model Based Iterative Refinement
- At inference, each denoising update is followed by a proximal data-consistency step that balances agreement with the limited-angle measurements.The data-fidelity subproblem can be solved with gradient-based methods.Source: §4.2 · p. 5
- DOLCE-SA averages multiple generated samples to approximate the conditional mean E[x|y].The method is designed to sample from the target posterior p(x|y).Source: §4.2 · p. 5
4.3. Model Architecture and Sampling Schedules
- The model adapts a guided-diffusion U-Net, while inference uses K < T spaced steps and tunes the schedule and proximal-step settings for PSNR.Training uses T = 2000 steps; the paper reports similar reconstruction quality with a cosine or uniform training noise schedule.Source: §4.3 · p. 5
5. Experiments
Experiments compare DOLCE with analytic, learned, and diffusion-based reconstructions on body CT and checked-in luggage, then examine cross-domain performance, uncertainty, data consistency, and 3D segmentation.
5.1. Datasets
- The experiments use checked-in luggage scans and kidney CT slices, with images resampled to 512 × 512.The luggage set contains 190 bags; the body CT data include scans from 210 patients.Source: §5.1 · p. 5
5.2. Training details and parameters
- A jointly trained DOLCE model uses FBP or RLS reconstructions at 60°, 90°, or 120° as conditional inputs; models trained separately on each dataset provide additional comparisons.The datasets are rescaled to a common intensity range for joint training, and the reported models use their latest checkpoints.Source: §5.2 · p. 6
5.3. Quantitative and Qualitative Results
- Across 150 test slices per dataset, DOLCE significantly outperforms existing approaches and unconditionally trained diffusion methods; visual results show sharper reconstructions with fine details.The comparisons cover body CT and checked-in luggage, with average PSNR and SSIM reported for each dataset.Source: Table 1 · p. 5, Figure 3 · p. 6, §5.3 · p. 7
5.4. Ablation Studies
- The jointly trained model is remarkably consistent in matching separately trained models across luggage and medical images.Table 3 compares average PSNR and SSIM for the combined-data model and the two separately trained models.Source: Table 3 · p. 7, §5.4 · p. 8
- DOLCE’s variance estimates are highly correlated with reconstruction errors, and more ill-posed inputs generally produce higher variance in generated samples.The conditional mean supplies the error estimate, while variance is represented as per-pixel standard deviation.Source: Figure 4 · p. 7, §5.4 · p. 8
- Data-consistency mapping improves reconstruction quality with fewer sampling steps, while proximal mapping lowers likelihood during inference.PSNR levels off after K = 50 iterations in the reported comparison.Source: §5.4 · p. 8, Figure 5 · p. 8
5.5. 3D Segmentation from CT Reconstructions
- In 3D segmentation of a 274-slice luggage scan, DOLCE preserves object boundaries better than RLS and DPS and more closely resembles the ground truth.The comparison uses region-growing segmentation on reconstructions made with θmax = 90°.Source: §5.5 · p. 8, Figure 6 · p. 8
6. Conclusion
DOLCE combines a conditional diffusion prior with forward-model data consistency to reconstruct limited-angle CT images. Experiments report strong performance across body and luggage images and support uncertainty characterization from multiple reconstructions.
6. Conclusion
- DOLCE is reported to achieve state-of-the-art performance across human-body and checked-in-luggage image distributions.The conclusion describes the method as enabling highly generalizable LACT reconstruction networks.Source: §6 · pp. 8–9
- The framework conditions a diffusion image prior on transformed limited-angle sinograms and applies a proximal data-consistency update during inference.The conditional input can be an FBP or RLS image, combining forward-model and prior constraints.Source: §6 · p. 8
- DOLCE’s diverse realizations from a given sinogram support systematic uncertainty characterization.The conclusion identifies this as a direction for diffusion models in severely ill-posed imaging problems.Source: §6 · p. 9
A. CT Reconstruction Formulation
The appendix describes parallel-beam CT projections and how reconstruction uses them. It explains how restricting the angular range removes edge information and blurs FBP reconstructions.
A. CT Reconstruction Formulation
- At each rotation angle, CT measures attenuated X-rays at detector positions, with projections representing line integrals of attenuation values.The object is rotated and imaged at regular angular intervals.Source: A. CT Reconstruction Formulation · p. 13, Figure 7 · p. 13
- The projection data Sθ(r, z) are called a sinogram, and the projection relation is separable along z.The relation therefore acts as a 2D function in the x–y plane, repeatedly applied along the z-axis.Source: A. CT Reconstruction Formulation · p. 13
- Filtered back-projection filters each projection and smears its contribution across the x–y plane; full-view reconstruction sums contributions over angles from 0 to π.Each filtered projection is smeared along direction (π/2 − θ).Source: A. CT Reconstruction Formulation · p. 13
- With limited-angle acquisition, missing edge information from unmeasured angles causes edge blur in FBP reconstructions.When acquisition stops at θmax < π, the edge information from angles θ ∈ [θmax, π] is absent.Source: A. CT Reconstruction Formulation · p. 13
B. Additional Implementation Details
The additional implementation details describe how CTNet, DPIR, ILVR, and DPS were adapted or configured, and identify the datasets and metrics used for supplementary evaluations.
B. Additional Implementation Details
- CTNet predicts invisible sinogram data with a GAN; its 128 × 128 outputs are super-resolved to 512 × 512 using a diffusion model.The diffusion model is trained for this upscaling step so CTNet outputs match the dimensions of the other methods.Source: B. Additional Implementation Details · p. 13
- DPIR’s denoiser is trained separately on each dataset for AWGN removal at noise levels σ ∈ [0, 5].The authors modify the public implementation and use similar settings at inference.Source: B. Additional Implementation Details · p. 13
- ILVR and DPS are adapted to the LACT forward model, with hyperparameters fine-tuned by grid search.The search is similar to the one used for DOLCE.Source: B. Additional Implementation Details · p. 13
- Tables 4 and 5 report average PSNR and SSIM against ground truth for medical body CT and checked-in luggage, respectively.Source: Table 4 · p. 14, Table 5 · p. 14
- The authors train the diffusion models used in the paper and show random samples from the unconditional 512 × 512 models for luggage and medical images.The samples are presented to illustrate the quality of the models used by ILVR and DPS.Source: B. Additional Implementation Details · p. 14
C. Additional Numerical and Visual Results
Additional experiments examine DOLCE’s performance under model mismatch, conditional-input and data-consistency choices, and uncertainty estimation, alongside further visual comparisons.
C. Additional Numerical and Visual Results
- RLS conditional input further boosts DOLCE beyond FBP input, and proximal-mapping data consistency improves reconstruction-sample quality.Tables 4 and 5 provide additional numerical evaluations across 60°, 90°, and 120° angular ranges.Source: C. Additional Numerical and Visual… · p. 14
- DOLCE consistently outperforms FBP, RLS, ILVR, and DPS when pretrained models are tested on 45°, 50°, or 55° limited-angle data.The comparison covers body CT and luggage datasets.Source: C. Additional Numerical and Visual… · p. 14, Table 6 · p. 15, Table 7 · p. 15
- Visual comparisons include body CT and luggage reconstructions at 60°, with additional comparisons of DOLCE and DOLCE-SA against DPIR and U-Net.The evaluations also include comparisons with FBP, ILVR, and DPS.Source: C. Additional Numerical and Visual… · p. 15
- DOLCE’s estimated variances are correlated with reconstruction errors and can serve as an error proxy when ground truth is unavailable.Figures 14–16 provide additional uncertainty-quantification results.Source: C. Additional Numerical and Visual… · p. 15
D. 3D Segmentation Results
The section evaluates whether DOLCE reconstructions support luggage-object segmentation, using region growing on reconstructed slices and comparing the results with reference segmentations.
D. 3D Segmentation Results
- DOLCE-based segmentations resemble ground-truth segmentations more closely than those obtained from FBP, TV, and DPS reconstructions.The comparison also includes segmentations from full-view ground truth and luggage labels.Source: D. 3D Segmentation Results · p. 15
- The evaluation combines reconstructed slices into 3D bags and uses region growing with a random start, fixed kernel size, and hand-tuned intensity thresholds.Thresholds ranged from 0.0001 to 0.02, and results use the best-performing setting because some reconstructions were poor and threshold-sensitive.Source: D. 3D Segmentation Results · p. 15
- Figures 17–21 show region-growing segmentations for test bags 2–6 against 3D renderings of reconstructed slices, using 60° or 90° angular coverage.Source: Figure 17 · p. 25, Figure 18 · p. 26, Figure 19 · p. 27