Credits

Citations

denoise is built on four papers. If you use this tool, please cite all four (Laugros:25 only when using --mode 3d).

[A1] — the core Noise2Inverse method

This paper introduces the algorithm that denoise is built on. The key insight is that two CT reconstructions produced from interleaved angular subsets (even and odd projections) are statistically independent. A U-Net trained to predict one from the other learns to suppress noise without any clean reference images. The paper provides the theoretical guarantee: when the measured noise is element-wise independent and zero-mean, this self-supervised training recovers a true denoising function. On simulated CT datasets it outperforms Total-Variation Minimisation and state-of-the-art image denoising methods in both PSNR and SSIM. denoise prepare automates the creation of the two input sub-reconstructions required by this method.

[B1] — 2.5D extension and multi-dimensional generalisation

This paper extends Noise2Inverse from single-slice (2D) processing to multi-dimensional domains — space, time, and spectrum. The 2.5D variant (a small stack of adjacent axial slices as input channels) exploits inter-slice coherence to suppress ring and streak artefacts more effectively than slice-by-slice processing. denoise implements this 2.5D architecture directly: the n_slices parameter in the config controls how many neighbouring slices are stacked. The paper also demonstrates applicability to dynamic micro-tomography and X-ray diffraction tomography on real-world synchrotron datasets.

[A2] — 3D U-Net architecture (used in –mode 3d)

This paper introduces a self-supervised image restoration pipeline for coherent X-ray neuronal microscopy (XNH), where structured 3D noise from probe-object mixing is correlated across slices and cannot be removed by 2D or 2.5D processing. The architecture is a full 3D U-Net with skip connections, layer normalisation, and 24-rotation cubic-symmetry data augmentation. denoise adopts this network directly in --mode 3d (see model3d.py); the default hyperparameters written by denoise prepare (psz_3d=96, n_blocks_3d=4, start_filts_3d=56, nb_patches_3d=17600) match the SSD_3D reference configuration from this paper.

[B2] — enhanced model selection and multi-checkpoint training

The original Noise2Inverse method trains for a fixed number of epochs, which can both miss the optimal model and waste computational resources. This paper proposes saving multiple checkpoints based on different criteria evaluated during training: validation reconstruction similarity, structural similarity (SSIM), PSNR, and cosine similarity between the two sub-reconstruction outputs. The best model identified this way improves SSIM and PSNR by up to 12.5% and 12.53%, respectively, while requiring only one-fifth of the training time. denoise implements this directly through three independently tracked checkpoints, each updated whenever a new best is found:

  • best_val_model.pth — lowest validation L1 loss

  • best_lcl_model.pth — lowest Laplacian Contrast Loss (LCL)

  • best_edge_model.pth — highest Laplacian edge score

The LCL term, added after a warm-up phase, penalises loss of high-frequency edge detail — a further contribution of this work. All three checkpoints are usable for inference at any point, even after an interrupted training run.

[A1]

Allard Adriaan Hendriksen, Daniël Maria Pelt, and K Joost Batenburg. Noise2inverse: self-supervised deep convolutional denoising for tomography. IEEE Transactions on Computational Imaging, 6:1320–1335, 2020. doi:10.1109/TCI.2020.3019647.

[A2]

Alfred Laugros, Peter Cloetens, Carles Bosch, Richard Schoonhoven, Liam Pavlovic, Aaron T. Kuan, Jayde Livingstone, Yuxin Zhang, Minsu Kim, Allard Hendriksen, Mirko Holler, Adrian A. Wanner, Anthony Azevedo, K. Joost Batenburg, John C. Tuthill, Wei-Chung Allen Lee, Andreas T. Schaefer, Nicola Vigano, and Alexandra Pacureanu. Self-supervised image restoration in coherent x-ray neuronal microscopy. bioRxiv, 2025. doi:10.1101/2025.02.10.633538.

Reference

[B1]

Allard A Hendriksen, Minna Bührer, Laura Leone, Marco Merlini, Nicola Vigano, Daniël M Pelt, Federica Marone, Marco Di Michiel, and K Joost Batenburg. Deep denoising for multi-dimensional synchrotron x-ray tomography without high-quality reference data. Scientific Reports, 11(1):11895, 2021. doi:10.1038/s41598-021-91084-8.

[B2]

Austin Yunker, Peter Kenesei, Hemant Sharma, Jun-Sang Park, Antonino Miceli, and Rajkumar Kettimuthu. Boosting noise2inverse via enhanced model selection for denoising computed tomography data. Tomography of Materials and Structures, pages 100075, 2025. doi:10.1016/j.tmater.2025.100075.