CosAE: Learnable Fourier Series for Image Restoration

In this paper, we introduce Cosine Autoencoder (CosAE), a novel, generic Autoencoder that seamlessly leverages the classic Fourier series with a feed-forward neural network. CosAE represents an input image as a series of 2D Cosine time series, each defined by a tuple of learnable frequency and Fourier coefficients. This method stands in contrast to a conventional Autoencoder that often sacrifices detail in their reduced-resolution bottleneck latent spaces. CosAE, however, encodes frequency coefficients, i.e., the amplitudes and phases, in its bottleneck. This encoding enables extreme spatial compression, e.g., $64\times$ downsampled feature maps in the bottleneck, without losing detail upon decoding. We showcase the advantage of CosAE via extensive experiments on flexible-resolution super-resolution and blind image restoration, two highly challenging tasks that demand the restoration network to effectively generalize to complex and even unknown image degradations. Our method surpasses state-of-the-art approaches, highlighting its capability to learn a generalizable representation for image restoration. The project page is maintained at [https://sifeiliu.net/CosAE-page/](https://sifeiliu.net/CosAE-page/).