# A signal processing interpretation of noise-reduction convolutional neural networks

arXiv: https://arxiv.org/abs/2307.13425 · HTML: https://mlsanity.com/paper/2307.13425/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 54 references that are in the map.
- First posted on arXiv 25 Jul 2023.

## Builds on (most cited first, 20 of 20)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [Robust and interpretable blind image denoising via bias-free convolutional neural networks](https://mlsanity.com/paper/1906.05478/) (2019)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [CNN-Based Projected Gradient Descent for Consistent Image Reconstruction](https://mlsanity.com/paper/1709.01809/) (2017)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [Convolutional Neural Networks Analyzed via Convolutional Sparse Coding](https://mlsanity.com/paper/1607.08194/) (2016)
- [Nonlinear Approximation and (Deep) ReLU Networks](https://mlsanity.com/paper/1905.02199/) (2019)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [Deep K-SVD Denoising](https://mlsanity.com/paper/1909.13164/) (2019)
- [Cycle-free CycleGAN using Invertible Generator for Unsupervised Low-Dose CT Denoising](https://mlsanity.com/paper/2104.08538/) (2021)
- [Understanding Geometry of Encoder-Decoder CNNs](https://mlsanity.com/paper/1901.07647/) (2019)
- [DCT2net: an interpretable shallow CNN for image denoising](https://mlsanity.com/paper/2107.14803/) (2021)
- [From Kernel Methods to Neural Networks: A Unifying Variational Formulation](https://mlsanity.com/paper/2206.14625/) (2022)

## Abstract (arXiv)

Encoding-decoding CNNs play a central role in data-driven noise reduction and can be found within numerous deep-learning algorithms. However, the development of these CNN architectures is often done in ad-hoc fashion and theoretical underpinnings for important design choices is generally lacking. Up to this moment there are different existing relevant works that strive to explain the internal operation of these CNNs. Still, these ideas are either scattered and/or may require significant expertise to be accessible for a bigger audience. In order to open up this exciting field, this article builds intuition on the theory of deep convolutional framelets and explains diverse ED CNN architectures in a unified theoretical framework. By connecting basic principles from signal processing to the field of deep learning, this self-contained material offers significant guidance for designing robust and efficient novel CNN architectures.