Exploring the Low-Pass Filtering Behavior in Image Super-Resolution

Deep neural networks for image super-resolution have shown significant advantages over traditional approaches like interpolation. However, they are often criticized as `black boxes' compared to traditional approaches which have solid mathematical foundations. In this paper, we attempt to interpret the behavior of deep neural networks using theories from signal processing theories. We first report an intriguing phenomenon, referred to as `the sinc phenomenon,' which occurs when an impulse input is fed to a neural network. Building on this observation, we propose a method named Hybird Response Analysis (HyRA) to analyze the behavior of neural networks in image super-resolution tasks. In details, HyRA decomposes a neural network into a parallel connection of a linear system and a non-linear system, demonstrating that the linear system functions as a low-pass filter, while the non-linear system injects high-frequency information. Furthermore, to quantify the injected high-frequency information, we introduce a metric for image-to-image tasks called Frequency Spectrum Distribution Similarity (FSDS). FSDS reflects the distribution similarity of different frequency components, capturing nuances that traditional metrics may overlook. Code for this work can be found in: https://github.com/RisingEntropy/LPFInISR.