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Noise2Match: Self-Supervised Low-Dose CT Denoising via Adaptive Inter-Slice Matching

Langrui Zhou, Guang Li, Xinyu Huang, Ziteng Zhou, Zuyang Huang, Hongming Shan, Shouhua Luo, Ning Gu

arXiv:2610.18379v1cs.CV

TL;DR

Paired clean targets are difficult to obtain, and existing self-supervised approaches face challenges with correlated LDCT noise and adjacent-slice misalignment. Noise2Match learns inter-slice transitions and corrects denoiser outputs; it outperforms image-domain self-supervised methods across LDCT tasks, particularly low-dose CBCT, and is reported as effective for image-domain CBCT denoising.

  • Problem

    Paired noisy-clean data are difficult to obtain, while adjacent-slice self-supervision can fail to satisfy the equal-mean condition because anatomical variation misaligns corresponding tissues.

    Source: §I · pp. 1–2

  • Method

    Noise2Match uses an inter-slice matching network to model label transitions and correct denoiser outputs, with loss reweighting to further enhance performance.

    Source: §I · p. 2, §IV · p. 16

  • Results

    Noise2Match achieves superior performance over state-of-the-art image-domain self-supervised methods across LDCT tasks, particularly low-dose CBCT, and is reported as the first effective image-domain self-supervised method for low-dose CBCT.

    Source: §I · p. 3, §IV · p. 16

  • Takeaways & Limitations

    The authors conclude that Noise2Match offers broader applicability and practical value, including self-supervised denoising directly in the image domain for low-dose CBCT.

    Source: §I · p. 3

Abstract

from arXiv · show

With the rapid development of deep learning, supervised convolutional neural network methods have greatly improved the performance of low-dose computed tomography (CT) denoising. However, they require paired noisy-clean training data, which is difficult to obtain in practice. Some classic self-supervised denoising methods rely on the assumption of pixel-wise independent noise, making them ineffective for correlated noise in low-dose CT (LDCT) images. Considering the high similarity and weaker noise correlation between adjacent CT slices, several recently proposed self-supervised methods use adjacent LDCT slices for training. Nevertheless, these approaches fail to effectively account for the non-rigid misalignment between slices caused by anatomical variation, hindering them from satisfying the equal-mean condition required by the classic Noise2Noise framework. In this paper, we propose Noise2Match, a self-supervised LDCT denoising method based on adaptive inter-slice matching. Noise2Match introduces an inter-slice matching network to model the label transition process between adjacent slices, and then applies correction to the denoiser's outputs to better satisfy the equal-mean condition. We theoretically prove that, under idealized conditions, training Noise2Match using adjacent LDCT slices is equivalent to supervised training with paired noisy-clean images. We further find that Noise2Match can also effectively perform low-dose conebeam CT (CBCT) denoising, which could be attributed to its correction operation that reduces inter-slice noise correlation. To the best of our knowledge, Noise2Match is the first effective image-domain self-supervised method for low-dose CBCT. Extensive experiments demonstrate that Noise2Match outperforms existing image-domain selfsupervised methods, offering broader applicability and higher practical value.

I. INTRODUCTION

Noise2Match addresses the difficulty of obtaining paired training data and the limits of self-supervised denoising under correlated LDCT noise. It adapts adjacent-slice supervision to non-rigid anatomical misalignment and reports strong LDCT results, including image-domain CBCT denoising.

I. INTRODUCTION

  • Paired noisy-clean training data can be expensive, time-consuming, or infeasible to obtain, while common single-image self-supervised methods assume pixel-wise independent noise and struggle with correlated LDCT noise.Adjacent-slice methods also face non-rigid misalignment: same-coordinate regions can belong to different tissues, undermining the equal-mean condition.Source: §I · pp. 1–2, Figure 1 · p. 2
  • Adjacent CT slices contain corresponding regions with shared true values and tend to have more independent noise, motivating their use for self-supervised LDCT denoising.Prior approaches include multi-slice guidance, similarity-thresholded pixel pairs, and filtering adjacent slices by noise correlation.Source: §I · p. 2
  • Noise2Match outperforms conventional denoising algorithms and state-of-the-art self-supervised methods, and is reported as the first effective image-domain self-supervised method for low-dose CBCT.Experiments on multiple datasets support the performance comparison; the authors attribute CBCT effectiveness potentially to correction that reduces inter-slice noise correlation.Source: §I · pp. 2–3
  • A matching network models label transitions between adjacent slices and corrects denoiser outputs to accommodate non-rigid anatomical misalignment.The authors prove equivalence to supervised training with paired noisy-clean images under idealized conditions.Source: §I · pp. 2–3, Figure 2 · p. 3

1) Noise2Noise Revisit:

  • Noise2Noise shows that, in expectation, training on independent zero-mean noisy observations of the same scene is equivalent to training against the clean image.Adjacent slices offer approximate paired samples because anatomy is spatially continuous, but longitudinal variation makes same-coordinate matching challenging.Source: 1) Noise2Noise Revisit · p. 3

2) Learning with Unreliable Labels:

Adjacent-slice self-supervision can be viewed as learning from unreliable labels because anatomical misalignment prevents direct pixelwise matching from reliably satisfying Noise2Noise’s equal-mean condition. Noise2Match corrects for estimated inter-slice transitions and, under idealized assumptions, its training is equivalent to supervised training with clean targets.

2) Learning with Unreliable Labels:

  • Directly comparing same-coordinate pixels across adjacent slices can pair different tissues, so misalignment can compromise the equal-mean condition and denoising constraints.Adjacent slices may have non-rigid anatomical misalignments; low dissimilarity at a coordinate does not guarantee the pixels belong to the same tissue.Source: 2) Learning with Unreliable Labels · pp. 3–4
  • A label transition matrix models the deformation mapping clean tissue values between adjacent slices, allowing denoiser outputs to be corrected before loss computation.The matrix represents a deformation field, with resampling denoted by ◦.Source: 2) Learning with Unreliable Labels · p. 4
  • Under idealized conditions, training on adjacent LDCT slices with corrected outputs is equivalent to supervised training on aligned noisy-clean pairs.The proof assumes independent zero-mean noises, matched locations with the same conditional noise distribution, a suitable deformation field, and denoiser equivariance.Source: 2) Learning with Unreliable Labels · p. 4
  • In practice, the equivalence is approximate because discrete-image interpolation and errors in the estimated transition matrix violate idealized assumptions.The theoretical result is stated for two-dimensional continuous-domain signals.Source: 2) Learning with Unreliable Labels · p. 4

B. Noise2Match

Noise2Match combines a denoising network with an inter-slice matching network that estimates transitions between adjacent slices from denoised outputs. Both networks are trained synchronously, while inference uses only the denoiser.

B. Noise2Match

  • Noise2Match uses a denoiser fθ and matching network Mϕ to estimate transitions between latent clean slices from the two denoised outputs.The method estimates transitions in both directions between adjacent slices.Source: B. Noise2Match · pp. 4–5
  • The method adopts symmetric training to use information from both adjacent noisy slices and stabilize training.The transition estimates have two channels for x- and y-direction offsets and the input images’ width and height.Source: B. Noise2Match · pp. 4–5
  • The denoiser and matching network are optimized synchronously through mutually reinforcing reconstruction and correction processes.The denoiser supplies cleaner references for matching, whose improved transition estimates in turn support reconstruction.Source: B. Noise2Match · p. 5
  • At inference, only the denoising network is retained, with no spatial warping or resampling of its output.Source: B. Noise2Match · p. 5

1) Reconstruction:

Noise2Match corrects denoised adjacent-slice outputs using estimated label transitions to better meet Noise2Noise’s equal-mean condition. A shared correction loss constrains denoising consistency and matching, while smoothness regularization discourages unnatural deformation fields.

1) Reconstruction:

  • The reconstruction loss compares denoised adjacent slices after warping one output into the other’s coordinates using estimated transition matrices.The loss is applied symmetrically in both directions.Source: 1) Reconstruction · p. 5
  • Detached transition estimates prevent reconstruction-loss gradients from optimizing the matching network along a competing path.The reconstruction loss could otherwise be minimized either by improving denoising or by fitting transition matrices to the loss.Source: 1) Reconstruction · p. 5
  • Even when matching is initially inaccurate, adjacent-slice similarity lets the denoiser learn approximate noise-suppression patterns from reconstruction loss.This supports continued denoiser improvement in early training.Source: 1) Reconstruction · p. 5

2) Correction:

  • The correction loss regularizes denoising consistency across matching tissue regions and guides the matching network to fit the transition process.It also encourages approximate denoiser equivariance, while an L2 penalty on spatial gradients regularizes transition fields against excessive distortion.Source: 2) Correction · p. 5

3) Loss Reweighting for Mismatched Pixels:

Noise2Match reweights losses to limit the influence of pixels that remain mismatched across adjacent slices. Reconstruction mismatches are zero-masked, while correction-loss values are instead constrained within a threshold.

3) Loss Reweighting for Mismatched Pixels:

  • A fixed threshold identifies regions with substantial differences between corrected denoised slices, and those pixels are zeroed in reconstruction-loss weights.The reweighting targets boundary cases where some pixels lack a same-value counterpart in the adjacent slice.Source: 3) Loss Reweighting for Mismatched… · p. 5
  • The training procedure samples adjacent LDCT images, estimates transition matrices, computes correction and smoothness losses, detaches transition estimates, then calculates reconstruction loss.Source: 3) Loss Reweighting for Mismatched… · p. 6
  • The overall objective combines reconstruction, correction, and smoothness losses, with hyperparameters controlling the latter two terms.Source: 3) Loss Reweighting for Mismatched… · p. 6
  • Correction-loss values are constrained within the threshold rather than zero-masked, allowing the matching network to continue optimizing mildly despite possible prediction errors.Source: 3) Loss Reweighting for Mismatched… · p. 6

A. Datasets

The experiments use clinical LDCT, single-volume LDCT, and low-dose CBCT datasets, alongside implementation and evaluation comparisons.

1) Mayo 2016 Dataset:

  • Mayo 2016 provides 5,936 noisy-clean image pairs from 10 patients; 5,326 slices from nine patients train models and 610 slices from one patient test them.Images are 512 × 512, with 1 mm slice thickness.Source: 1) Mayo 2016 Dataset · p. 6

2) Mayo 2020 Dataset:

  • Mayo 2020 abdominal CT contributes 7,293 training slices from 45 patients and 866 test slices from five patients.The dataset contains paired noisy-clean scans from 299 patients; images are 512 × 512.Source: 2) Mayo 2020 Dataset · p. 6

3) Piglet Dataset:

  • The Piglet dataset contains 800 slices; self-supervised models train on 25%-dose images and are evaluated against normal-dose images.Each 512 × 512 slice has 0.63 × 0.63 mm2 pixels and 0.625 mm thickness.Source: 3) Piglet Dataset · p. 6

4) Real-World CBCT Dataset:

  • The Real-World CBCT dataset uses 1,167 low-dose images from one rat for training and 1,167 from another for testing, without corresponding NDCT references.Scans use isotropic 13 µm resolution; images are cropped to 1152 × 1152.Source: 4) Real-World CBCT Dataset · p. 6

5) ICASSP CBCT Dataset:

  • The ICASSP CBCT dataset simulates low-dose data for 1,010 patients using LIDC-IDRI chest CT as ground truth; 5,120 slices from 20 patients train and 768 from three test.The selected images are 256 × 256, with incident photons set to 105.Source: 5) ICASSP CBCT Dataset · p. 6

B. Implementation Details

  • Figure 3 presents qualitative method comparisons on Mayo 2016 and Mayo 2020, including NDCT ground truth and LDCT inputs.Source: Figure 3 · p. 7
  • All images are normalized to [0, 1] before being fed into the network.Source: B. Implementation Details · p. 7
  • Comparisons include BM3D, supervised RED-CNN and Noise2Clean, and self-supervised baselines; Noise2Clean shares Noise2Match’s denoising architecture but uses paired noisy-clean training.Evaluation uses PSNR, SSIM, and RMSE, computed from the denoiser output without matching, correction, or spatial resampling at inference.Source: B. Implementation Details · pp. 7–8

C. Performance Comparison on Clinical LDCT Datasets

Noise2Match is compared with other methods on clinical LDCT, single-volume LDCT, and CBCT. Across these settings, it combines noise suppression with structural preservation and achieves the strongest reported self-supervised quantitative performance.

C. Performance Comparison on Clinical LDCT Datasets

  • On Mayo 2016 and Mayo 2020, Noise2Match outperformed traditional and self-supervised methods, approached supervised performance, and beat Noise2Sim and SVB significantly on PSNR, SSIM, and RMSE (all p < 0.001).Qualitative results also report clear structural detail while suppressing noise.Source: C. Performance Comparison on Clinical… · p. 8

D. Performance Comparison on Single LDCT Volume

  • When trained directly on one LDCT volume, Noise2Match outperformed other self-supervised methods on Mayo 2016 and Piglet and better preserved low-contrast liver-lesion boundaries.The reported qualitative comparison also notes stronger content and structural preservation.Source: D. Performance Comparison on Single… · p. 9

E. Performance Comparison on Low-Dose CBCT Datasets

  • On both CBCT datasets, Noise2Match achieved the best quantitative performance among self-supervised methods while suppressing noise and preserving tissue contrast and structure.Real-World CBCT lacks clean references; its CNR and Std values are supplementary measurements from representative slices, not dataset-level metrics.Source: E. Performance Comparison on Low-Dose… · pp. 10–11

F. Analysis of Inter-Slice Noise Correlation

The analysis measures inter-slice noise correlation before and after Noise2Match’s correction across four datasets. Correlation falls substantially after correction, including under a control that distinguishes anatomical matching from resampling alone.

F. Analysis of Inter-Slice Noise Correlation

  • The correction experiment estimates label-transition matrices from trained denoiser and matching networks, then compares noise-patch |PCC| before and after warping.For Real-World CBCT, approximate noise maps come from subtracting a Gaussian-smoothed image; ROIs avoid visible anatomical edges.Source: F. Analysis of Inter-Slice Noise… · p. 11
  • After correction, mean inter-slice |PCC| decreased substantially across Mayo 2016, Mayo 2020, Real-World CBCT, and ICASSP CBCT.The analysis averages 500 ROI measurements per point; uncorrected CBCT noise correlation persists across multiple neighboring slices, unlike the more rapidly decaying clinical fan-beam CT correlation.Source: F. Analysis of Inter-Slice Noise… · p. 11
  • On Real-World CBCT at k = 2, correction reduced |PCC| to 0.0752±0.0206 with bilinear interpolation and 0.0691±0.0181 with nearest-neighbor interpolation, versus 0.2935±0.0377 originally.A fixed 0.5-pixel translation alone left |PCC| nearly unchanged at 0.2917±0.0414, indicating matching rather than interpolation chiefly reduced correlation.Source: F. Analysis of Inter-Slice Noise… · p. 12

G. Analysis of Learned Inter-Slice Deformation Fields

The learned deformation fields are evaluated for anatomical plausibility and spatial regularity. They align corresponding structures while showing no measured local folding across the four training datasets.

G. Analysis of Learned Inter-Slice Deformation Fields

  • The estimated fields vary continuously, concentrate larger displacements where adjacent slices differ anatomically, and improve spatial correspondence without apparent structural distortion.The figure presents denoised current and adjacent slices, the corrected current slice, and displacement magnitude in pixels.Source: G. Analysis of Learned Inter-Slice… · p. 12
  • The Jacobian determinant characterizes local transformation behavior, and non-positive values indicate folding or orientation reversal.The folding ratio counts spatial locations with non-positive Jacobian determinants.Source: G. Analysis of Learned Inter-Slice… · pp. 12–13
  • Folding ratio was 0% on Mayo 2016, Mayo 2020, Real-World CBCT, and ICASSP CBCT, with mean Jacobian determinants near 1 on every dataset.The reported means±standard deviations are 0.9999±0.0495, 1.0001±0.0727, 1.0002±0.0604, and 1.0007±0.0703, respectively.Source: G. Analysis of Learned Inter-Slice… · p. 13, Table IV · p. 13

H. Ablation Study

The ablations test component contributions and the sensitivity of inter-slice distance k and reweighting threshold th.

1) Ablation on Different Components:

  • Removing all components lowers PSNR by 2.22 dB and SSIM by 0.0181, and raises RMSE by 4.94 HU versus full Noise2Match.The full model achieves the best qualitative and quantitative results; the ablations also indicate benefits from the matching network, correction loss, smooth loss, and loss reweighting.Source: 1) Ablation on Different Components · p. 13, Table V · p. 13, Figure 10 · p. 13

2) Ablation on Different Parameter k:

3) Ablation on Different Parameter th for Loss Reweighting:

4) Empirical Evaluation of the Equivariance Condition:

The authors empirically assess the denoiser's equivariance condition and discuss Noise2Match's mechanisms and the limits of its theoretical equivalence.

4) Empirical Evaluation of the Equivariance Condition:

  • The two denoising paths are visually highly consistent, with only minor residual differences, indicating approximate equivariance for the estimated transition matrix.The compared paths apply the estimated deformation before or after denoising, respectively.Source: 4) Empirical Evaluation of the… · p. 15, Figure 13 · p. 15

IV. DISCUSSION AND CONCLUSION

  • The correction operation adapts supervision to non-rigid slice misalignment and can match pixels with weaker noise correlation, while loss reweighting mitigates mismatches at tissue boundaries.The authors relate these mechanisms to improved satisfaction of Noise2Noise's equal-mean condition and image-domain low-dose CBCT denoising.Source: §IV · p. 15
  • Noise2Match outperforms state-of-the-art image-domain self-supervised methods across multiple LDCT tasks, particularly low-dose CBCT, but its training objective is only approximately equivalent to supervised denoising in practice.The equivalence relies on idealized assumptions; discrete-image interpolation and errors in estimated transitions mean those assumptions are only approximately satisfied.Source: §IV · pp. 15–16

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