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Image Denoising Using Global and Local Circulant Representation

arXiv 2512.23569 ↗First posted 29 Dec 2025cs.CVcited by 0

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Abstract (arXiv)

The proliferation of imaging devices and countless image data generated every day impose an increasingly high demand on efficient and effective image denoising. In this paper, we establish a theoretical connection between principal component analysis (PCA) and the Haar transform under circulant representation, and present a computationally simple denoising algorithm. The proposed method, termed Haar-tSVD, exploits a unified tensor singular value decomposition (t-SVD) projection combined with Haar transform to efficiently capture global and local patch correlations. Haar-tSVD operates as a one-step, parallelizable plug-and-play denoiser that eliminates the need for learning local bases, thereby striking a balance between denoising speed and performance. Besides, an adaptive noise estimation scheme is introduced to improve robustness according to eigenvalue analysis of the circulant structure. To further enhance the performance under severe noise conditions, we integrate deep neural networks with Haar-tSVD based on the established Haar-PCA relationship. Experimental results on various denoising datasets demonstrate the efficiency and effectiveness of proposed method for noise removal. Our code is publicly available at https://github.com/ZhaomingKong/Haar-tSVD.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 43 of its 104 references that are in the map. First posted on arXiv 29 Dec 2025.

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43 of 104 references.

References · 43

  1. 2017Attention Is All You Needcited by 59,932
  2. 2015Deep Residual Learning for Image Recognitioncited by 51,809
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  4. 2021Restormer: Efficient Transformer for High-Resolution Image Restorationcited by 1,618
  5. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  6. 2014Image Super-Resolution Using Deep Convolutional Networkscited by 1,218
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  11. 2017Benchmarking Denoising Algorithms with Real Photographscited by 209
  12. 2020A Physics-based Noise Formation Model for Extreme Low-light Raw Denoisingcited by 138
31 more
  1. 2019FastDVDnet: Towards Real-Time Deep Video Denoising Without Flow Estimationcited by 128
  2. 2022Blind2Unblind: Self-Supervised Image Denoising with Visible Blind Spotscited by 83
  3. 2020Supervised Raw Video Denoising with a Benchmark Dataset on Dynamic Scenescited by 77
  4. 2018Real-world Noisy Image Denoising: A New Benchmarkcited by 74
  5. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  6. 2015Exact tensor completion using t-SVDcited by 70
  7. 2016Efficient tensor completion for color image and video recovery: Low-rank tensor traincited by 61
  8. 2019DVDnet: A Fast Network for Deep Video Denoisingcited by 60
  9. 2020Unsupervised Deep Video Denoisingcited by 44
  10. 2024MaIR: A Locality- and Continuity-Preserving Mamba for Image Restorationcited by 43
  11. 2018A Trilateral Weighted Sparse Coding Scheme for Real-World Image Denoisingcited by 42
  12. 2017Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoisingcited by 41
  13. 2019ViDeNN: Deep Blind Video Denoisingcited by 40
  14. 2018Non-local Meets Global: An Integrated Paradigm for Hyperspectral Denoisingcited by 39
  15. 2023Spatially Adaptive Self-Supervised Learning for Real-World Image Denoisingcited by 33
  16. 2024Transfer CLIP for Generalizable Image Denoisingcited by 29
  17. 2022Unidirectional Video Denoising by Mimicking Backward Recurrent Modules with Look-ahead Forward Onescited by 24
  18. 2021Joint Denoising and Demosaicking with Green Channel Prior for Real-world Burst Imagescited by 18
  19. 2023Stimulating Diffusion Model for Image Denoising via Adaptive Embedding and Ensemblingcited by 17
  20. 2019NLH: A Blind Pixel-level Non-local Method for Real-world Image Denoisingcited by 15
  21. 2024Revisiting Nonlocal Self-Similarity from Continuous Representationcited by 14
  22. 2017External Prior Guided Internal Prior Learning for Real-World Noisy Image Denoisingcited by 12
  23. 2025IDF: Iterative Dynamic Filtering Networks for Generalizable Image Denoisingcited by 12
  24. 2017VIDOSAT: High-dimensional Sparsifying Transform Learning for Online Video Denoisingcited by 10
  25. 2019Color Image and Multispectral Image Denoising Using Block Diagonal Representationcited by 10
  26. 2024Rethinking Transformer-Based Blind-Spot Network for Self-Supervised Image Denoisingcited by 9
  27. 2023A Comparison of Image Denoising Methodscited by 7
  28. 2024Self-Calibrated Variance-Stabilizing Transformations for Real-World Image Denoisingcited by 4
  29. 2024Image Denoising Using Green Channel Priorcited by 4
  30. 2024Spatiotemporal Blind-Spot Network with Calibrated Flow Alignment for Self-Supervised Video Denoisingcited by 4
  31. 2024Beyond Image Prior: Embedding Noise Prior into Conditional Denoising Transformercited by 3

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