ButterflyNet2D: Bridging Classical Methods and Neural Network Methods in Image Processing
This work addresses image processing practitioners by offering a method that combines interpretability from classical approaches with neural network performance, though it appears incremental as it builds on existing CNN and Fourier techniques.
The paper tackled the problem of bridging classical Fourier transform-based methods and neural networks in image processing by introducing ButterflyNet2D, a CNN with sparse cross-channel connections and Fourier initialization, which achieved better performance than random initialization in four image processing tasks.
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.