# Efficient Image Denoising Using Global and Local Circulant Representation

arXiv: https://arxiv.org/abs/2508.10307 · HTML: https://mlsanity.com/paper/2508.10307/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 106 references that are in the map.
- First posted on arXiv 14 Aug 2025.

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

- [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)
- [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)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Toward Convolutional Blind Denoising of Real Photographs](https://mlsanity.com/paper/1807.04686/) (2018)
- [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)
- [AP-BSN: Self-Supervised Denoising for Real-World Images via Asymmetric PD and Blind-Spot Network](https://mlsanity.com/paper/2203.11799/) (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)
- [A Poisson-Gaussian Denoising Dataset with Real Fluorescence Microscopy Images](https://mlsanity.com/paper/1812.10366/) (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)
- [C2N: Practical Generative Noise Modeling for Real-World Denoising](https://mlsanity.com/paper/2202.09533/) (2022)
- [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)

## Abstract (arXiv)

The advancement of imaging devices and countless image data generated everyday impose an increasingly high demand on efficient and effective image denoising. In this paper, we present a computationally simple denoising algorithm, termed Haar-tSVD, aiming to explore the nonlocal self-similarity prior and leverage the connection between principal component analysis (PCA) and the Haar transform under circulant representation. We show that global and local patch correlations can be effectively captured through a unified tensor-singular value decomposition (t-SVD) projection with the Haar transform. This results in a one-step, highly parallelizable filtering method that eliminates the need for learning local bases to represent image patches, striking a balance between denoising speed and performance. Furthermore, we introduce an adaptive noise estimation scheme based on a CNN estimator and eigenvalue analysis to enhance the robustness and adaptability of the proposed method. Experiments on different real-world denoising tasks validate the efficiency and effectiveness of Haar-tSVD for noise removal and detail preservation. Datasets, code and results are publicly available at https://github.com/ZhaomingKong/Haar-tSVD.