# Deep K-SVD Denoising

arXiv: https://arxiv.org/abs/1909.13164 · HTML: https://mlsanity.com/paper/1909.13164/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2019.

## Built on by (most cited first, 26 of 26)

- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [CVF-SID: Cyclic multi-Variate Function for Self-Supervised Image Denoising by Disentangling Noise from Image](https://mlsanity.com/paper/2203.13009/) (2022)
- [Patch2Self: Denoising Diffusion MRI with Self-Supervised Learning](https://mlsanity.com/paper/2011.01355/) (2020)
- [Revisiting Sparse Convolutional Model for Visual Recognition](https://mlsanity.com/paper/2210.12945/) (2022)
- [Operator SVD with Neural Networks via Nested Low-Rank Approximation](https://mlsanity.com/paper/2402.03655/) (2024)
- [Understanding approximate and unrolled dictionary learning for pattern recovery](https://mlsanity.com/paper/2106.06338/) (2021)
- [DCT2net: an interpretable shallow CNN for image denoising](https://mlsanity.com/paper/2107.14803/) (2021)
- [SC-MIL: Sparsely Coded Multiple Instance Learning for Whole Slide Image Classification](https://mlsanity.com/paper/2311.00048/) (2023)
- [Adaptive and Implicit Regularization for Matrix Completion](https://mlsanity.com/paper/2208.05640/) (2022)
- [Connections between Deep Equilibrium and Sparse Representation Models with Application to Hyperspectral Image Denoising](https://mlsanity.com/paper/2203.15901/) (2022)
- [CDLNet: Noise-Adaptive Convolutional Dictionary Learning Network for Blind Denoising and Demosaicing](https://mlsanity.com/paper/2112.00913/) (2021)
- [Meta-Optimization of Deep CNN for Image Denoising Using LSTM](https://mlsanity.com/paper/2107.06845/) (2021)
- [Gabor is Enough: Interpretable Deep Denoising with a Gabor Synthesis Dictionary Prior](https://mlsanity.com/paper/2204.11146/) (2022)
- [Learning spatially adaptive sparsity level maps for arbitrary convolutional dictionaries](https://mlsanity.com/paper/2602.21707/) (2026)
- [Denoising and Optical and SAR Image Classifications Based on Feature Extraction and Sparse Representation](https://mlsanity.com/paper/2106.01896/) (2021)
- [Dense-Sparse Deep Convolutional Neural Networks Training for Image Denoising](https://mlsanity.com/paper/2107.04857/) (2021)
- [Details Preserving Deep Collaborative Filtering-Based Method for Image Denoising](https://mlsanity.com/paper/2107.05115/) (2021)
- [AIR-Net: Adaptive and Implicit Regularization Neural Network for Matrix Completion](https://mlsanity.com/paper/2110.07557/) (2021)
- [Decay2Distill: Leveraging spatial perturbation and regularization for self-supervised image denoising](https://mlsanity.com/paper/2208.01948/) (2022)
- [A signal processing interpretation of noise-reduction convolutional neural networks](https://mlsanity.com/paper/2307.13425/) (2023)
- [Anchor Space Optimal Transport as a Fast Solution to Multiple Optimal Transport Problems](https://mlsanity.com/paper/2310.16123/) (2023)
- [Analysis and Synthesis Denoisers for Forward-Backward Plug-and-Play Algorithms](https://mlsanity.com/paper/2411.13276/) (2024)
- [CbLDM: A Diffusion Model for recovering nanostructure from atomic pair distribution function](https://mlsanity.com/paper/2509.01370/) (2025)
- [RoseCDL: Robust and Scalable Convolutional Dictionary Learning for Rare event and Anomaly Detection](https://mlsanity.com/paper/2509.07523/) (2025)
- [Missing No More: Dictionary-Guided Cross-Modal Image Fusion under Missing Infrared](https://mlsanity.com/paper/2603.08018/) (2026)
- [Quasi-SVD: Learning a Lie-constrained matrix factorisation for real-time imaging](https://mlsanity.com/paper/2607.25967/) (2026)

## Abstract (arXiv)

This work considers noise removal from images, focusing on the well known K-SVD denoising algorithm. This sparsity-based method was proposed in 2006, and for a short while it was considered as state-of-the-art. However, over the years it has been surpassed by other methods, including the recent deep-learning-based newcomers. The question we address in this paper is whether K-SVD was brought to its peak in its original conception, or whether it can be made competitive again. The approach we take in answering this question is to redesign the algorithm to operate in a supervised manner. More specifically, we propose an end-to-end deep architecture with the exact K-SVD computational path, and train it for optimized denoising. Our work shows how to overcome difficulties arising in turning the K-SVD scheme into a differentiable, and thus learnable, machine. With a small number of parameters to learn and while preserving the original K-SVD essence, the proposed architecture is shown to outperform the classical K-SVD algorithm substantially, and getting closer to recent state-of-the-art learning-based denoising methods. Adopting a broader context, this work touches on themes around the design of deep-learning solutions for image processing tasks, while paving a bridge between classic methods and novel deep-learning-based ones.