  In the generator of typical Generative Adversarial Networks (GANs), a noise
is inputted to generate fake samples via a series of convolutional operations.
However, current noise generation models merely relies on the information from
the pixel space, which increases the difficulty to approach the target
distribution. Fortunately, the long proven wavelet transformation is able to
decompose multiple spectral information from the images. In this work, we
propose a novel multi-channel wavelet-based filtering method for GANs, to cope
with this problem. When embedding a wavelet deconvolution layer in the
generator, the resultant GAN, called WaveletGAN, takes advantage of the wavelet
deconvolution to learn a filtering with multiple channels, which can
efficiently homogenize the generated noise via an averaging operation, so as to
generate high-fidelity samples. We conducted benchmark experiments on the
Fashion-MNIST, KMNIST and SVHN datasets through an open GAN benchmark tool. The
results show that WaveletGAN has excellent performance in generating
high-fidelity samples, thanks to the smallest FIDs obtained on these datasets.
