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A deep dictionary network-based foundation model for ultra-low-dose CT denoising

Baoshun Shi, Shuangyi Yang, Ke Jiang, Bin Zhu, Zhanli Hu, Huazhu Fu

arXiv:2609.16031v1eess.IVcs.CVcs.LG

TL;DR

Organ-specific denoisers generalize poorly across heterogeneous multi-organ ULDCT, and existing foundation-model architectures have limited interpretability. This paper proposes a DDN-based foundation model with sparse-representation layers and denoising pre-training. Experiments report strong denoising performance across organs, cross-organ settings, real data, and few-shot evaluation.

  • Problem

    Organ-specific denoisers have limited generalization across heterogeneous multi-organ ULDCT, while existing foundation-model architectures are difficult to interpret.

    Source: §I · p. 1

  • Method

    The DDN foundation model combines multilayer sparse-coding layers with dynamic dictionaries, adaptive thresholds, and large-scale denoising pre-training with sparse regularization.

    Source: §I · p. 2

  • Results

    Experiments report superior denoising performance and generalization across multiple organs, cross-organ settings, real experimental data, and few-shot evaluation.

    Source: §I · p. 2, 1) Quantitative results · p. 7, 2) Qualitative results · p. 7

  • Takeaways & Limitations

    The experiments support DDN as a unified approach to multi-organ ULDCT denoising with transferable priors and strong performance across the evaluated settings.

    Source: §I · p. 2, §VI · p. 10

Abstract

from arXiv · show

Ultra-low-dose computed tomography (ULDCT) reduces radiation exposure but suffers from severe noise that degrades diagnostic image quality. Existing deep learning-based denoising methods are typically trained in an organ-specific fashion, resulting in limited generalization across heterogeneous multi?organ imaging scenarios. Foundation models present a promising all-in-one paradigm for unified multi-organ denoising. However, their architectures suffer from poor interpretability and rely on heuristic training strategies. To address these limitations, we propose an architecture?interpretable foundation model based on the deep dictionary network (DDN) for unified multi-organ ULDCT denoising. Inspired by multilayer sparse representation theory, DDN cascades convolutional sparse coding layers with iterative soft-thresholding, providing inherent architectural interpretability. Furthermore, a dynamic dictionary module and a threshold generation module are embedded within each layer to enhance representation ability. We conduct DDN pre-training on more than one million multi-organ normal-dose CT images by recovering clean images from Gaussian-noised inputs. Sparse regularization is additionally imposed on latent feature representations, guiding the network to learn compact and noise-robust priors. The complete architecture is jointly fine-tuned on multi-organ ULDCT datasets, enabling a single unified model to perform denoising across diverse anatomical regions. Extensive experiments validate that our proposed method achieves state-of-the?art performance and consistently surpasses competing ULDCT methods across all mul

I. INTRODUCTION

ULDCT can reduce radiation exposure, but severe noise and artifacts degrade image quality, while organ-specific denoisers generalize poorly across heterogeneous organs. The paper proposes an interpretable DDN foundation model and reports strong multi-organ and few-shot denoising performance.

I. INTRODUCTION

  • Organ-specific denoisers increase storage and deployment costs and limit the use of shared CT priors across heterogeneous organs.The paper identifies this as a constraint on generalization in multi-organ ULDCT scenarios.Source: §I · p. 1
  • DDN combines multilayer sparse-representation unfolding with cascaded convolutional sparse-coding layers and iterative soft-thresholding for an interpretable multi-organ denoising backbone.The paper presents this as an alternative to foundation-model architectures with limited interpretability.Source: §I · pp. 1–2
  • The dynamic dictionary module generates input-dependent dictionary atoms, while the threshold generation module predicts spatially adaptive thresholds from local, large, non-local, and global features.These modules are designed to accommodate heterogeneous anatomy and spatially varying noise.Source: §I · p. 2
  • Pre-training on more than one million multi-organ normal-dose CT images recovers clean images from Gaussian-noised inputs and imposes an ℓ1 constraint on latent representations.The strategy is intended to promote compact, noise-robust, transferable priors for downstream denoising.Source: §I · p. 2
  • DDN consistently outperforms existing methods across anatomical regions on synthetic multi-organ ULDCT datasets and real experimental CT data.With only 20 training images per organ, it also achieves the best average PSNR and SSIM among compared methods.Source: §I · p. 2

II. EXISTING ULTRA-LOW-DOSE CT DENOISING METHODS

  • Traditional methods require parameter tuning and can be computationally costly; sinogram methods may introduce reconstruction artifacts, while dual-domain methods require projection data and imaging geometry.Image-domain methods do not require raw projections or scanner-specific parameters, but broader cross-organ generalization remains underexplored.Source: §II · p. 3

III. THE PROPOSED DEEP DICTIONARY NETWORK

Single-layer sparse coding seeks a sparse representation that approximates the input using an overcomplete dictionary. Its formulation balances reconstruction fidelity against sparsity, and ISTA solves it through iterative gradient and thresholding steps.

A. Single-layer sparse coding

  • Sparse coding seeks a sparse representation α such that Dα approximates input x, using an overcomplete dictionary.The formulation uses an ℓ1-regularized optimization objective.Source: A. Single-layer sparse coding · p. 3
  • The objective balances approximation error against sparsity, with λ controlling the trade-off between data fidelity and sparsity.The two terms measure reconstruction error and promote sparse coefficients, respectively.Source: A. Single-layer sparse coding · p. 3
  • ISTA solves the objective through alternating gradient descent and proximal mapping, with soft-thresholding setting coefficients below τ to zero and shrinking larger ones.The stated step size is 1/c, where c bounds the maximum eigenvalue of D^T D.Source: A. Single-layer sparse coding · p. 3

B. From single-layer sparse representation to deep sparse representation with dynamic dictionary

The method extends single-layer sparse coding into a hierarchy of dictionary layers and approximately solves the resulting deep sparse-coding problem with iterative updates. Input-dependent dynamic dictionaries replace static kernels to adapt the representation to image content.

B. From single-layer sparse representation to deep sparse representation with dynamic dictionary

  • Cascaded dictionary layers form hierarchical sparse representations, extending x ≈ D1α1 to x ≈ D1D2 · · · DJαJ.The final-layer representation is αJ, and dictionary parameters are learned through backpropagation.Source: B. From single-layer sparse… · p. 3
  • The deep sparse-coding problem is approximately solved iteratively, with each layer's subproblem handled by ISTA for L iterations.The architecture cascades J dictionary layers, each performing L updates.Source: B. From single-layer sparse… · pp. 3–4
  • The dynamic dictionary module generates input-dependent dictionary atoms, replacing static dictionaries to adapt each layer's representation to image content and heterogeneous anatomy.The architecture combines these dynamic dictionaries with iterative updates and adaptive soft-thresholding.Source: B. From single-layer sparse… · p. 4, Figure 2 · p. 4

C. Threshold generation module

The threshold generation module predicts a spatially adaptive threshold map from an initial coefficient estimate because a fixed scalar threshold cannot accommodate heterogeneous anatomy and spatially varying ULDCT noise. Its local and large sub-modules extract complementary detail and broader-context features.

C. Threshold generation module

  • The threshold generation module predicts a spatially adaptive map from an initial coefficient estimate, rather than using ISTA's globally fixed scalar threshold.The threshold map is intended to adapt to heterogeneous anatomy and spatially varying ULDCT noise.Source: C. Threshold generation module · p. 5

1) Local and large sub-modules:

  • The local sub-module uses successive 3 × 3 convolutions to capture edges and fine details, while 41 × 41 kernels in the large sub-module capture broader context and large-scale anatomy.The two feature outputs provide complementary information for threshold generation.Source: 1) Local and large sub-modules · p. 5

2) Non-local sub-module:

The threshold-generation design combines local, large-scale, non-local, and global information. Its non-local module models long-range dependencies, while the global module contributes layout-level features to the adaptive threshold map.

2) Non-local sub-module:

  • The non-local sub-module uses window-based self-attention and shifted-window interaction to model long-range dependencies that convolutions capture poorly.Projected sparse features pass through channel-attention transformer blocks comprising channel-attention blocks and locally enhanced feed-forward networks.Source: 2) Non-local sub-module · p. 5
  • The non-local feature output fuses the bottleneck feature with the encoder feature through decoder channel-attention transformer blocks.An output projection produces the resulting feature output.Source: 2) Non-local sub-module · p. 5

3) Global sub-module:

  • The global sub-module downsamples features to 32 × 32 and uses a U-shaped vision Mamba block with representation and weighting paths to model global dependencies.The paths refine a global representation and generate adaptive weights that modulate feature importance.Source: 3) Global sub-module · p. 5
  • The four sub-module outputs are summed and fused by a 1 × 1 convolution and sigmoid to produce a spatially adaptive threshold map.That threshold map is shared across soft-thresholding operations within its dictionary layer.Source: 3) Global sub-module · p. 5

D. Overall architecture of the proposed DDN

DDN cascades dictionary layers with iterative updates and adaptive dictionaries and thresholds for unified multi-organ ULDCT denoising. Its pre-training uses noisy-to-clean CT recovery with sparse regularization to learn compact, noise-robust representations.

D. Overall architecture of the proposed DDN

  • DDN cascades dictionary layers and iterative updates, replacing conventional static dictionaries and fixed thresholds with input-dependent dictionaries and thresholds informed by local, large, non-local, and global features.The architecture combines multilayer sparse-representation interpretability with adaptability for unified multi-organ ULDCT denoising.Source: D. Overall architecture of the… · p. 5

IV. THE PROPOSED FOUNDATION MODEL TRAINING STRATEGY

  • Pre-training uses more than one million multi-organ normal-dose CT images, recovering clean images from Gaussian-noised inputs.This objective aligns pre-training with ULDCT denoising.Source: §IV · p. 5
  • The pre-training objective combines image-denoising loss with an ℓ1 penalty on the final sparse representation to encourage compact sparse coefficients.The denoising loss is mean squared error between the denoised image and clean target.Source: §IV · p. 6
  • Pre-training is described as learning compact, noise-robust representations that provide effective initialization for downstream multi-organ ULDCT denoising.The final latent sparse representation is produced by mapping the noisy image through cascaded sparse coding.Source: §IV · pp. 5–6

1) Pre-training datasets:

The pre-training corpus spans over one million CT images and multiple anatomical regions. ULDCT evaluation uses simulated datasets, external cross-organ datasets, and experimentally acquired data.

1) Pre-training datasets:

  • 1,126,182 CT images from ten public multi-organ datasets are used for pre-training, covering the head, chest, abdomen, and spine.Images are clipped, resized to 512 × 512, normalized, and stored in H5 format.Source: 1) Pre-training datasets · p. 6

2) Ultra-low-dose CT datasets:

  • Five datasets provide simulated ULDCT data, while KiTS19, MSD Pancreas Tumours, and experimentally acquired CT data support external cross-organ and practical-condition evaluation.The five simulation datasets are CQ500 and four MSD tasks: Hepatic Vessel, Lung Tumours, Spleen, and Colon Cancer.Source: 2) Ultra-low-dose CT datasets · p. 6
  • For the 1/10 dose setting, fixed photon counts vary by organ: 1×104 for head, 1.2×104 for lung/colon, and 4 × 103 for spleen/hepatic vessel.The incident photon flux is modeled using organ type and organ-specific tube current.Source: 2) Ultra-low-dose CT datasets · p. 6
  • Simulation forward-projects normal-dose images, injects Poisson noise into measurements, and reconstructs noisy sinograms with FBP; each organ has 1,000 training and 100 each validation and test images.The reconstructed images are normalized to [0, 1].Source: 2) Ultra-low-dose CT datasets · p. 6

1) Pre-training details:

  • Blind-noise pre-training samples σ from [0, 75] and optimizes denoising loss plus final-representation ℓ1 regularization weighted 1 × 10−2.Training uses Adam, batch size 8, and eight NVIDIA GeForce RTX 4090 GPUs.Source: 1) Pre-training details · p. 6

2) ULDCT denoising network training details:

DDN is initialized from pre-training and jointly fine-tuned with a decoder on multi-organ ULDCT data. It leads the five-organ average comparison and preserves anatomical detail in the illustrated lung case.

2) ULDCT denoising network training details:

  • The pretrained DDN is jointly fine-tuned with an attached decoder that maps sparse representations back to image space.Training uses mean squared error; PSNR, SSIM, and RMSE are used for quantitative evaluation.Source: 2) ULDCT denoising network training… · pp. 6–7

1) Quantitative results:

C. Comparison with previous methods on internal datasets

  • Comparisons include traditional denoising, foundation-model, and all-in-one methods, trained on the same five-organ mixed dataset using released implementations.DDN uses MoCE-Dec, the decoder module of MoCE-IR.Source: C. Comparison with previous methods on… · p. 7

2) Qualitative results:

  • On the representative lung case, DDN suppresses noise while preserving clearer boundaries and subtle anatomical details than the compared methods.The comparison uses enlarged regions to inspect noise suppression and anatomical structure preservation.Source: 2) Qualitative results · p. 7, Figure 3 · p. 7

1) Generalization on external datasets:

DDN generalizes to external kidney and pancreas data and real experimental scans, while pretrained initialization improves performance across decoder designs. The few-shot subsection tests training with only 20 images per organ.

2) Generalization on real experimental data:

  • On real pork-with-bone data, DDN more effectively suppresses noise while preserving structural integrity and fine local details than competing methods.Other methods show residual noise, over-smoothing, and loss of subtle structures, particularly around low-contrast boundaries.Source: Figure 5 · p. 8, 2) Generalization on real experimental… · p. 8

1) Generalization on external datasets:

E. Effect of decoder design and foundation model

  • Pretrained DDN initialization improves PSNR and SSIM across decoder settings, while MoCE-Dec with initialization achieves the best overall results.The evaluated configurations include Conv41, Conv41 with two additional dictionary layers, and MoCE-Dec.Source: E. Effect of decoder design and… · pp. 8–9, Figure 6 · p. 9

F. Few-shot learning

  • The few-shot experiment retrains all learning-based methods using only 20 training images per organ, with validation and test sets unchanged.The supplied passages describe this evaluation setup but do not report its results.Source: F. Few-shot learning · p. 9

1) Comparison with previous methods:

With only 20 training images per organ, DDN outperforms competing methods, and pretrained initialization improves results across decoder designs. Ablations support the contributions of dictionary depth, dynamic dictionaries, and threshold-generation features.

1) Comparison with previous methods:

  • In few-shot denoising, DDN improves average PSNR by 2.02 dB and SSIM by 0.0138 over MoCE-IR, with pretrained sparse representations providing effective restoration priors when downstream data are limited.Fig. 7 compares visual results for a representative colon case under the few-shot setting, with enlarged regions for local anatomical structures.Source: 1) Comparison with previous methods · p. 9, Figure 7 · p. 9

2) Effect of decoder design and foundation model:

  • Foundation-model initialization improves PSNR and SSIM across three decoder configurations, with overall gains of approximately 3 dB and 0.03, respectively.MoCE-Dec with initialization achieves the best average PSNR of 41.30 dB and SSIM of 0.9695.Source: Figure 8 · p. 9, 2) Effect of decoder design and… · p. 9

G. Ablation studies

  • Increasing dictionary depth progressively improves denoising, and the complete three-layer DDN performs best; replacing dynamic atoms with static kernels lowers PSNR from 42.99 dB to 42.23 dB.Table III reports ablation results averaged over the test datasets.Source: G. Ablation studies · p. 9, Table III · p. 10
  • Removing any TGM sub-module degrades performance; removing the non-local sub-module causes the largest decrease, reducing PSNR by 1.72 dB.The authors attribute complementary threshold-generation cues to local, large, non-local, and global feature information.Source: G. Ablation studies · p. 10, Table III · p. 10

VI. CONCLUSION

  • The conclusion identifies artifact reduction and super-resolution as future CT restoration tasks for extending the DDN-based framework.Source: §VI · p. 10
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