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.

翻译：深度神经网络在图像超分辨率任务中相较于插值等传统方法展现出显著优势。然而，与传统方法拥有坚实的数学基础不同，这些网络常被诟病为“黑箱”。本文尝试利用信号处理理论解释深度神经网络的行为。我们首先报告一个有趣的现象，称为“sinc现象”，该现象发生在脉冲输入馈入神经网络时。基于此观察，我们提出一种名为混合响应分析（HyRA）的方法，用于分析神经网络在图像超分辨率任务中的行为。具体而言，HyRA将神经网络分解为线性系统与非线性系统的并联连接，表明线性系统起低通滤波器作用，而非线性系统则注入高频信息。此外，为量化注入的高频信息，我们引入一种面向图像到图像任务的度量指标——频谱分布相似度（FSDS）。FSDS反映不同频率分量的分布相似性，能够捕捉传统度量可能忽视的细微差异。本工作代码可在以下链接获取：https://github.com/RisingEntropy/LPFInISR。