# DCT2net: an interpretable shallow CNN for image denoising

arXiv: https://arxiv.org/abs/2107.14803 · HTML: https://mlsanity.com/paper/2107.14803/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 31 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Non-Local Recurrent Network for Image Restoration](https://mlsanity.com/paper/1806.02919/) (2018)
- [Neural Nearest Neighbors Networks](https://mlsanity.com/paper/1810.12575/) (2018)
- [Deep K-SVD Denoising](https://mlsanity.com/paper/1909.13164/) (2019)

## Built on by (most cited first, 6 of 6)

- [Linear Combinations of Patches are Unreasonably Effective for Single-Image Denoising](https://mlsanity.com/paper/2212.00422/) (2022)
- [Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction](https://mlsanity.com/paper/2412.13070/) (2024)
- [A signal processing interpretation of noise-reduction convolutional neural networks](https://mlsanity.com/paper/2307.13425/) (2023)
- [A unified framework of non-local parametric methods for image denoising](https://mlsanity.com/paper/2402.13816/) (2024)
- [RHVI-FDD: A Hierarchical Decoupling Framework for Low-Light Image Enhancement](https://mlsanity.com/paper/2604.05781/) (2026)
- [A Study of the Limits of Collaborative DCT-Based Image Denoising via Interpretable Neural Networks](https://mlsanity.com/paper/2609.29334/) (2026)

## Abstract (arXiv)

This work tackles the issue of noise removal from images, focusing on the well-known DCT image denoising algorithm. The latter, stemming from signal processing, has been well studied over the years. Though very simple, it is still used in crucial parts of state-of-the-art "traditional" denoising algorithms such as BM3D. Since a few years however, deep convolutional neural networks (CNN) have outperformed their traditional counterparts, making signal processing methods less attractive. In this paper, we demonstrate that a DCT denoiser can be seen as a shallow CNN and thereby its original linear transform can be tuned through gradient descent in a supervised manner, improving considerably its performance. This gives birth to a fully interpretable CNN called DCT2net. To deal with remaining artifacts induced by DCT2net, an original hybrid solution between DCT and DCT2net is proposed combining the best that these two methods can offer; DCT2net is selected to process non-stationary image patches while DCT is optimal for piecewise smooth patches. Experiments on artificially noisy images demonstrate that two-layer DCT2net provides comparable results to BM3D and is as fast as DnCNN algorithm composed of more than a dozen of layers.