# ButterflyNet2D: Bridging Classical Methods and Neural Network Methods in Image Processing

arXiv: https://arxiv.org/abs/2211.16578 · HTML: https://mlsanity.com/paper/2211.16578/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [CoTr: Efficiently Bridging CNN and Transformer for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.03024/) (2021)
- [Learning Fast Algorithms for Linear Transforms Using Butterfly Factorizations](https://mlsanity.com/paper/1903.05895/) (2019)
- [Pixelated Butterfly: Simple and Efficient Sparse training for Neural Network Models](https://mlsanity.com/paper/2112.00029/) (2021)
- [Effects of Image Degradations to CNN-based Image Classification](https://mlsanity.com/paper/1810.05552/) (2018)
- [Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks](https://mlsanity.com/paper/1805.07451/) (2018)
- [Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform Initialization](https://mlsanity.com/paper/1912.04154/) (2019)

## Abstract (arXiv)

Both classical Fourier transform-based methods and neural network methods are widely used in image processing tasks. The former has better interpretability, whereas the latter often achieves better performance in practice. This paper introduces ButterflyNet2D, a regular CNN with sparse cross-channel connections. A Fourier initialization strategy for ButterflyNet2D is proposed to approximate Fourier transforms. Numerical experiments validate the accuracy of ButterflyNet2D approximating both the Fourier and the inverse Fourier transforms. Moreover, through four image processing tasks and image datasets, we show that training ButterflyNet2D from Fourier initialization does achieve better performance than random initialized neural networks.