# Image Denoising Using Global and Local Circulant Representation

arXiv: https://arxiv.org/abs/2512.23569 · HTML: https://mlsanity.com/paper/2512.23569/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 104 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Builds on (most cited first, 30 of 43)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [VRT: A Video Restoration Transformer](https://mlsanity.com/paper/2201.12288/) (2022)
- [Benchmarking Denoising Algorithms with Real Photographs](https://mlsanity.com/paper/1707.01313/) (2017)
- [A Physics-based Noise Formation Model for Extreme Low-light Raw Denoising](https://mlsanity.com/paper/2003.12751/) (2020)
- [FastDVDnet: Towards Real-Time Deep Video Denoising Without Flow Estimation](https://mlsanity.com/paper/1907.01361/) (2019)
- [Blind2Unblind: Self-Supervised Image Denoising with Visible Blind Spots](https://mlsanity.com/paper/2203.06967/) (2022)
- [Supervised Raw Video Denoising with a Benchmark Dataset on Dynamic Scenes](https://mlsanity.com/paper/2003.14013/) (2020)
- [Real-world Noisy Image Denoising: A New Benchmark](https://mlsanity.com/paper/1804.02603/) (2018)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [DVDnet: A Fast Network for Deep Video Denoising](https://mlsanity.com/paper/1906.11890/) (2019)
- [MaIR: A Locality- and Continuity-Preserving Mamba for Image Restoration](https://mlsanity.com/paper/2412.20066/) (2024)
- [Unsupervised Deep Video Denoising](https://mlsanity.com/paper/2011.15045/) (2020)
- [A Trilateral Weighted Sparse Coding Scheme for Real-World Image Denoising](https://mlsanity.com/paper/1807.04364/) (2018)
- [Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising](https://mlsanity.com/paper/1705.09912/) (2017)
- [ViDeNN: Deep Blind Video Denoising](https://mlsanity.com/paper/1904.10898/) (2019)
- [Non-local Meets Global: An Integrated Paradigm for Hyperspectral Denoising](https://mlsanity.com/paper/1812.04243/) (2018)
- [Spatially Adaptive Self-Supervised Learning for Real-World Image Denoising](https://mlsanity.com/paper/2303.14934/) (2023)
- [Transfer CLIP for Generalizable Image Denoising](https://mlsanity.com/paper/2403.15132/) (2024)
- [Unidirectional Video Denoising by Mimicking Backward Recurrent Modules with Look-ahead Forward Ones](https://mlsanity.com/paper/2204.05532/) (2022)
- [Joint Denoising and Demosaicking with Green Channel Prior for Real-world Burst Images](https://mlsanity.com/paper/2101.09870/) (2021)

## 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.