MR-Net: Multiresolution sinusoidal neural networks.

We present MR-Net, a general architecture for multiresolution sinusoidal neural networks, and a framework for imaging applications based on this architecture. We extend sinusoidal networks, and we build an infrastructure to train networks to represent signals in multiresolution. Our coordinate-based networks, namely L-Net, M-Net, and S-Net, are continuous both in space and in scale as they are composed of multiple stages that progressively add finer details. Currently, band-limited coordinate networks (BACON) are able to represent signals at multiscale by limiting their Fourier spectra. However, this approach introduces artifacts leading to an image with a ringing effect. We show that MR-Net can represent more faithfully what is expected of sequentially applying low-pass filters in a high-resolution image. Our experiments on the Kodak Dataset show that MR-Net can reach comparable Peak Signal-to-Noise Ratio (PSNR) to other architectures, on image reconstruction, while needing fewer additional parameters for multiresolution. Along with MR-Net, we detail our architecture's mathematical foundations and general ideas, and show examples of applications to texture magnification, minification, and antialiasing. Lastly, we compare our three MR-Net subclasses. [Display omitted] • Framework to train deep networks to represent signals in multiresolution. • Network initialization is used to control the frequencies learned by the model. • MR-Net provides a continuous representation of signals spatially and in scale. • MR-Net represents images with higher or comparable PSNR than other architectures. • Applications in texture magnification and minification, and antialiasing. [ABSTRACT FROM AUTHOR]