Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform
Structured CNN designed using the prior information of problems potentially
improves efficiency over conventional CNNs in various tasks in solving PDEs and
inverse problems in signal processing. This paper introduces BNet2, a
simplified Butterfly-Net and inline with the conventional CNN. Moreover, a
Fourier transform initialization is proposed for both BNet2 and CNN with
guaranteed approximation power to represent the Fourier transform operator.
Experimentally, BNet2 and the Fourier transform initialization strategy are
tested on various tasks, including approximating Fourier transform operator,
end-to-end solvers of linear and nonlinear PDEs, and denoising and deblurring
of 1D signals. On all tasks, under the same initialization, BNet2 achieves
similar accuracy as CNN but has fewer parameters. And Fourier transform
initialized BNet2 and CNN consistently improve the training and testing
accuracy over the randomly initialized CNN.